Page 306 - Geothermal Energy Systems Exploration, Development, and Utilization

282 5 Geothermal Reservoir Simulation
the past, such as continua approaches (e.g., Barenblatt et al. (1990)) and discrete
fracture approaches (e.g., Witherspoon et al. (1980); Brown (1987)) as well as
combinations of both. The Soultz geothermal reservoir is located in crystalline
rocks, where water flows mainly through fractures. Therefore, we are dealing with
deterministic discrete fracture models in the following.
The Soultz-sous-Forets HDR site is located in the upper Rhine valley between
the Black Forest and Vosges mountains (Figure 5.1). Soultz is one of the most
investigated geothermal research locations (Jung 1991; Baria 1992; Baria et al.,
1999; Weidler et al., 2002; Baria et al., 2006; Valley and Evans, 2007; Schindler et al.,
2008). The applicability of Darcy’s law for groundwater flow (equation) to fractured
rock is limited in particular in the vicinity of injection and production wells.
Hydraulic testing at Soultz, for example, the pumping tests 94JUN16 and 94JUL04
showed that nonlinear flow behavior must be taken into account (Kohl et al., 1997).
For describing nonlinear flow behavior we use the Forchheimer equation (5.4).
In addition to possible nonlinear flow behavior we have to take into account that
rock fractures are not plane. Fracture roughness can cause flow channeling effects
(Figure 5.26). A detailed study of nonlinear flow in fractured rock can be found in
Kolditz (2001)
On the basis of the pumping test 95JUL01 (Jung et al., 1995) investigated the
nonlinear flow behavior in a fracture network system (Kolditz, 2001). Figure 5.27
shows the numerical analysis of the pumping test. Circles illustrate measured data
and solid lines mark simulated pressure for both cases of linear flow (Darcy) and
nonlinear flow (Forchheimer). Linear flow behavior shows a linear relationship
between pumping rate increase and corresponding pressure increase to force the
fluid volume through the system (lower solid curve in Figure 5.27). The pumping
test clearly indicates nonlinear flow behavior. The flow rates of the four steps
increase nearly in a linear stepwise way: 6, 13, 19, and 26 l/s. As can be seen from
Figure 5.27, the pressure increase is nearly quadratical. The calibrated permeability
values are close to that found by Kohl et al. (1997). The storativity values however
differ. Note, storativity values by Kohl et al. (1997) correspond to the rock matrix,
whereas storativity in this study corresponds to the fracture system. In fact, this
is the conceptual difference between both models. (Kohl et al., 1997) assumed that
fluid canbestored inthe rock matrix.Inthisstudy we found thatinthe short
timescale of the experiment fluid loss into the rock matrix must be very small and,
therefore, it was assumed that the fluid is stored in the fracture system. If relating
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both storativity values by the rock porosity of about n = 10 , it can be seen that
the volume of storable fluid is comparable for both models.
From Figure 5.27, it can be seen that the pumping test data are well matched
by using the nonlinear flow model except the shut-off period. During this period,
fluid pressure is decreasing to the hydrostatic level. The overestimated pressure
drawdown means that the storativity of the reservoir is underestimated in the
shut-off period. This indicates storativity changes during the hydraulic tests. This
can be explained with the increased volume of the stimulated fracture system.
Because of small relative displacements of rough fracture surfaces during pressure
increase they will not close perfectly after reducing the reservoir pressure again.