Page 294 - Geothermal Energy Systems Exploration, Development, and Utilization

270 5 Geothermal Reservoir Simulation
we assume linear depth-dependent hydrostatic pressure, lithostatic stress, and
temperature distribution. The geothermal gradient according to the temperature
−1
logs in the reservoir depth range of U3 is ω = 0.3K m :
• T(t = 0) = 435.15 + ω (−4445.0 − z)(K)
l
l
• p (t = 0) = ρ gz (Pa)
s
• σ zz (t = 0) = ρ gz (Pa)
s
• σ xx (t = 0) = σ yy (t = 0) = νρ gz (Pa)
The injection well is considered to have an overpressure of 10 MPa and the
production well an underpressure of 10 MPa. Fluid injection temperature is
◦
assumed to be 50 C(McDermott et al., 2006).
• T in = 323.15 (K)
in
6
• p = p 0 + 10 × 10 (Pa)
6
• p out = p 0 − 10 × 10 (Pa)
• u · n = 0 at the lateral and bottom surface
• ∂σzz = ρ gz at the top surface
s
dz
We use a FE model for the stochastic analysis, which takes into account fully
coupled THM processes according to the governing equations given in Section 5.2.
The present code provides an object-oriented FE concept; different element types
can be easily used for THM analysis. The characteristic element length is about
20 m resulting in 6600 elements and 7920 nodes for the hexahedra mesh and
59 599 elements and 11 856 nodes for the tetrahedra mesh. Grid adaptation is
necessary in order to resolve the boreholes geometrically and to obtain a smooth
change of element sizes.

5.6.1.2 Simulation Results
A parameter sensitivity analysis for an undisturbed reservoir using the fully coupled
THM model confirmed that the most important parameters are permeability and
fluid viscosity for reservoir hydraulics, as well as heat capacity for reservoir
thermodynamics.

5.6.1.3 Stimulated Reservoir Model
(Watanabe et al., 2009) analyzed the statistical sensitivity of THM parameters as
well as variogram properties in detail. Besides parameter uncertainty, a realistic
reservoir model should address the effect of reservoir stimulation as well. As
a result of massive hydraulic stimulation, the reservoir permeability could be
increased by factor of 100, at least in the vicinity of the boreholes (Baisch et al.,
2004). The stimulation length is in the order of 100–200 m. In this section,
we conduct a Monte Carlo analysis to assess the thermal reservoir evolution
by a superposition of stochastic parameter heterogeneity and hydraulic reservoir
stimulation. We represent the heterogeneity of the undisturbed reservoir using
a spherical variogram model with a correlation length of 50 m range. Hydraulic
stimulation is mimicked by a scaling factor between 1 (undisturbed) and 100 (fully
stimulated), which depends on the borehole distance.