Page 273 - Geothermal Energy Systems Exploration, Development, and Utilization

5.2 Theory 249

Hydrogeological Unconsolidated and fractured aquifers
system
Conceptual model Fracture model Continuum model
Model geometry Single and multiple Fracture network Multiple porous media
fractures (deterministic,stochastic)

~ 200° C (~ 3 hm)

~Sa10 m
Total -1 -1
surface
~ 300° C (~ 4.5 hm)

y'
x'
1 1
~1.5×10 m
Total surface

Sources Cornet (1985) Kolditz (1994a) Stober (1986)
Bruel & Cacas (1992)

Figure 5.2 Conceptual models for fractured rock (Kolditz, 1997).
Material properties of geothermal fluids are nonlinear functions of salinity, tem-
perature, and pressure (McDermott et al., 2006). More details on THM mechanics
can be found, for example, in Lewis and Schrefler (1998); Ehlers and Bluhm (2002);
Wang and Kolditz (2007).

5.2.2.1 Heat Transport
For the heat transport problem, we consider advective and diffusive fluxes in
saturated porous and fractured media. The difference between porous and frac-
tured media is the flow calculation according to Darcy’s (Equation (5.3)) and
Forchheimer’s law (Equation 5.4), respectively. The governing equation of heat
transport is
∂T l l
cρ + c ρ v ·∇T −∇(λ∇T) = Q T (5.1)
∂t
with following porous media properties
s s
l l
cρ = nc ρ + (1 − n)c ρ
l
λ = nλ + (1 − n)λ s (5.2)