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248 5 Geothermal Reservoir Simulation
be given by the simple Kriging estimate of the unknown value and its associated
error variance. Before starting stochastic simulations, assumptions concerning
parameter distribution, for example, histogram, spatial correlation, correlation
with other parameters, have to be decided. Usually these assumptions are deter-
mined from site observation data. However, little information about histogram and
variogram analysis for deep crystalline rocks is available in the literature.

5.2
Theory

In this section, we briefly introduce the conceptual models for geothermal reservoir
simulation as well as summarize the governing equations of THM processes in
fractured porous media. The constitutive equations for the reservoir character-
ization including geothermal fluid properties are presented in the subsequent
Section 5.3. The list of symbols can be found at the end of this chapter.

5.2.1
Conceptual Approaches

Figure 5.2 depicts an overview of existing modeling concepts for geothermal
reservoir simulation of both fractured and porous media. Before fracture network
models have been introduced into geothermal reservoir simulation (Bruel and
Cacas, 1992; Bruel et al., 1994), more simple geometric concepts such as single and
parallel fracture systems have been investigated, for example, (Cornet, 1985). The
alternative for modeling fractured rock is the use of equivalent porous media, for
example, (Stober, 1986). The behavior of rock masses is significantly influenced
by fractures; therefore, many efforts have been undertaken to develop appropriate
numerical methods for the representation of fractures (Cacas et al., 1990). Fracture
network models are a closer representation of geological reality as real rock masses
are penetrated by different fracture populations. Figure 5.2 shows two different
concepts for fracture network modeling, deterministic and stochastic approaches.
Stochastic models are based on the statistic properties of the fracture network
observed in borehole loggings. Monte Carlo methods with a representative number
of different realizations are used in order to investigate, for example, the hydraulic
behavior of fracture networks (Bruel et al., 1994). Deterministic models deal with a
few number of major fractures in order to study the interaction between fractures
and rock matrix, for example, for heat extraction processes (Kolditz, 1995).

5.2.2
THM Mechanics

The physical processes involved are nonisothermal saturated flow, heat transport,
and thermoporoelastic deformation. The corresponding field variables of the mul-
tifield problem are liquid phase pressure, temperature, and displacement vector.