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saturated and confined on top and             FIGURE 2. Result after 30 years of heat production, showing the hydraulic connection
bottom by aquitards (impermeable beds).       between the production and injection zones and temperature distribution along the flow paths.
This model represents a case where there      FIGURE 3. Graph showing the production temperature after reaching stationary flow
are fully-saturated and mainly pressure-      conditions as a function of the lateral distance
driven flows, so Darcy’s law can be used
to describe the geothermal strata. In
situations where a partially-saturated
zone needs to be modeled, Richards’
equations would be used instead.

   Geothermal groundwater is pumped
through the production well at a rate
of 50 liters per second. The well is
represented as an empty cylinder in
the geometry to allow inlet and outlet
boundary conditions for fluid flow. After
the extracted water is used for heat or
power generation, it is re-injected at the
same rate but with a lower temperature
(in this case 5°C).

   Figure 2 shows the resulting flow field
and temperature distribution in the well
after 30 years of heat production.

   The model is an appropriate tool
for estimating the development of a
geothermal site under varied conditions.
For example, it can answer questions such
as: How is the production temperature
affected by the lateral distance of the
wells? Is it worthwhile to reach a large
spread or is a moderate distance sufficient?

   Using this model, different borehole
systems can easily be analyzed by
changing the positions of the injection/
production cylinders in the geometry.
Figure 3 shows the production
temperature of the well for different well
distances, demonstrating how the model
can be used to determine at what distance
the highest temperature, and thus the
most energy, can be produced.

   In the first example, an aquifer without
ambient groundwater movement
was analyzed. What happens if there
is a hydraulic gradient that leads to
groundwater flow?

   Figure 4 shows the same situation as the
previous example after 20 years, except
with a hydraulic head gradient of 0.01 m,
which creates a flow field.

èREDUCING PROSPECTING                         FIGURE 4. Single borehole after 30 years of heat production and overlapping
RISK UNCERTAINTY                              groundwater flow due to a horizontal pressure gradient.

By using a model such as this one, many
different situations and environments can
be analyzed. Due to the multiphysics nature
of the model, additional physics types can
easily be added to the simulation, helping
to provide an accurate description of the
environment within a borehole, predict its
useful lifespan, and provide an estimate of
the prospecting risks. v

                                              COMSOL NEWS                                                                  29
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