Geothermal energy is an important and sustainable
resource that has more potential than is currently utilized. Whether or not
a deep geothermal resource can be exploited, mostly depends on, besides
temperature, the utilizable reservoir volume over time, which in turn
largely depends on petrophysical parameters. We show, using over 1000 (
The amount of geothermal energy that can be extracted from a reservoir depends, to a 1st-order approximation, on reservoir temperature, permeability, and utilizable reservoir volume. While temperature is often well constrained, permeability and the utilizable reservoir volume are more difficult to predict (e.g. Bauer, 2018; Bauer et al., 2017; Kushnir et al., 2018; Laubach et al., 2009; Seeburger and Zoback, 1982). The most important parameters recognized in the literature are porosity and permeability (e.g. Agemar et al., 2014; Moeck, 2014; Tiab and Donaldson, 2004). They are often highly heterogeneous because of layering, localized fracturing, and diagenesis (e.g. Aragón-Aguilar et al., 2017; De Marsily, 1986; Manning and Ingebritsen, 1999; Zhang, 2013). The vast majority of hydrothermal systems can be considered dual-porosity systems, where porosity is provided by both pore space and fractures (Gringarten, 1984; Warren and Root, 1963).
In sedimentary geothermal reservoirs, the matrix porosity can exceed 30 %
and is often highly variable, even on a small scale, e.g. within or between
different sedimentary layers (e.g. Bär, 2012; Bauer et al., 2017; Heap
at al., 2017; Zhang, 2013). Fracture porosity of sedimentary rocks, in
contrast, is commonly significantly lower than matrix porosity and rarely
exceeds 0.001 % (e.g. Snow, 1968; van Golf-Racht, 1982). Nevertheless,
permeability, and therefore flow rate in geothermal reservoirs, is
dominantly controlled by fractures (e.g. Bear, 1993; De Marsily, 1986;
Hestir and Long, 1990; Nelson, 1985). Intrinsic fracture permeability is
determined by the cube of the fracture aperture, while the permeability of
fractured and porous reservoirs is related to the fracture system and the
connection between fractures and pore space (De Marsily, 1986; Odling et
al., 1999; Ran et al., 2014). Importantly, geometry, spatial distribution of
fractures, and the resulting permeability anisotropy of a fracture system
are difficult to predict (e.g. Laubach et al., 2014; Ortega and Marrett,
2000; Watkins et al., 2018). A number of deep geothermal projects in
southern Germany (e.g. Trebur (Erdwerk, 2019), Mauerstetten (iTG, 2019), and Geretsried
(iTG)) were unsuccessful because they failed to predict the hydraulic
properties of the fracture system(s). In addition, there have been cases
where, after a successful initial phase, the temperature of the production
fluid dropped unexpectedly. Several of these cases were observed in faulted
reservoirs, where production and injection wells were placed within a
highly permeable fault damage zone (e.g. Bödvarsson and Tsang, 1982;
Diaz et al., 2016; Horne, 1982a, b; MacDonald et al., 1992; Ocampo et al.,
1998; Parini et al., 1996; Tenma et al., 2008). These fault zone
permeabilities are often highly variable, i.e. they have been reported to
reach from about 10
Geothermal reservoirs are also affected by other factors, such as the
background hydraulic gradient (BHG) and its interaction with the artificial
flow field caused by the production. The BHG is, to our best knowledge,
often not considered in model studies of geothermal systems, even though it
may strongly affect the reservoir lifetime (Bense et al., 2013; Hochstein,
1988; Moeck, 2014). Hydraulic gradients generated by groundwater recharge
and discharge at the land surface average 1 % (10 mm m
Here, we present a non-site-specific sensitivity analysis of a 4-D finite-element model of fluid and heat flow in a reservoir that comprises more than 1000 individual model runs. The objective of our study is to quantify the effects of various parameters on the temperature development of a geothermal reservoir and to quantify to what extent these parameters should be known to allow for reliable estimates on the lifetime of a geothermal reservoir. In addition, we evaluate under which circumstances a closed geothermal system can be achieved, i.e. when the injection and production well doublet is hydraulically connected.
To achieve these objectives, we examine the importance of porosity, permeability, and permeability anisotropy on reservoir lifetime. We systematically test the effects of all these parameters for homogenous, layered, fractured, and faulted reservoirs. Furthermore, we apply BHGs of different magnitudes and orientations to each of the different reservoir configurations.
The values for porosity and permeability that were included covered a range
that is considered desirable for geothermal reservoirs but also included
values that lie above and below these values. Specifically, we used
permeabilities of 10
We simulated fluid and heat flows for a geothermal doublet, with one
injection well and one production well, over a time span of 200 years. The model
results quantify the effect of different geological parameters on the
lifetime of a geothermal reservoir, i.e. the time during which the
temperature of the produced fluid is above a critical value. As a benchmark
for the reservoir performance, we chose to record the time before the
production temperature reaches 100
The numerical model experiments were carried out using finite-element
modelling (FEM) with the COMSOL Multiphysics® 5.0 software
package (Comsol, 2019), including the subsurface flow module for fluid flow in porous
media and for heat flow (COMSOL Multiphysics®). Fluid and
heat flow were modelled by solving the following equations:
The velocity field,
Model setup used in our study.
The modelled volume measures
We applied a linear geothermal gradient of 0.047
The top and bottom boundaries were thermally isolated: heat flux
through these boundaries was set to zero. This approximation ignores the
background geothermal heat flux. However, over the comparatively short model
time (200 years), a background heat flux of 65 mW m
The upper and lower model boundaries were closed to fluid flow. A BHG was simulated in the model, which was varied in magnitude and direction in different model runs. The BHG was applied as a pressure gradient on the model boundaries from different directions and is thus valid for the whole model domain (Fig. 1b).
We applied a specified flow rate of 75 L s
The temperature of the reinjected fluid was set to 40
Material properties used for all models. The rock and fluid
properties are oriented on Triassic Buntsandstein sandstone and a geothermal
brine, respectively. Rock properties are adopted from Bär (2012); the
fluid properties are typical for geothermal brine at 100
Permeability was implemented using the continuum approach, which is, for sufficiently large volumes, a reasonable approximation (e.g. Berkowitz et al., 1988). In the continuum approach, hydraulic properties are assigned to a replacement media, which has the mean hydraulic properties of a given fracture system. In our study, the parameters porosity and permeability are not coupled, because we vary each parameter separately. Therefore, we do not consider the role of effective porosity. Lithostatic pore pressures affect only fluid flow, but not permeability or porosity. Porosity controls the heat capacity of a given volume. Since fracture porosity is typically not higher than 0.001 % (e.g. Snow, 1968; van Golf-Racht, 1982) its contribution to heat capacity can be considered neglectable.
In the following, we define the basic model properties. Homogenous models do not include any internal structure; isotropic models do not contain fracture anisotropy. Four basic scenarios were investigated (Fig. 1c–f). Material properties used for all models are listed in Table 1.
In the first scenario (Scenario 1, Fig. 1c), the reservoir is homogenous and isotropic.
We evaluate the time to thermal breakthrough for all combinations of three
porosity values (
In the second scenario (Scenario 2, Fig. 1d), we introduced five horizontal confining
layers, each 100 m thick at intervals of 300 m, into the model volume. The
production- and injection wells were placed in a 300 m thick reservoir. This
scenario comprises three series with different reservoir permeabilities (
In the third scenario (Scenario 3, Fig. 1e), the model had a porosity of 14 %, and a
permeability of 10
To all possible variations of different parameters in these three scenarios,
we applied BHGs of 0, 1, 5, and 20 mm m
In the fourth scenario (Fig. 1f), we tested the effect of a N–S-striking,
60
In this fourth scenario, the orientations of the BHGs were 0,
90, 180, and 270
In total, we modelled 1027 experiments with increasing geological complexity. Note that since the range of permeabilities analysed was large, we kept other parameters, including the fluid injection rate, constant to allow different models to be comparable.
The modelled time was 200 years. In several cases, the production temperatures did not reach the threshold in this time, and therefore in these cases the reported lifetimes are underestimated and we give the breakthrough time to be equal or greater than 200 years.
Since in our sensitivity study we tested multiple parameters, we decided to
present the results of the different (sub)scenarios in multiple figures. In
all cases, scatter plots are presented next to each other, which contain the
same results. The
With our approach, we aim to examine how different reservoir parameters and their interaction affect the lifetime of geothermal reservoirs. Thus, our study is not site specific but rather investigates, using simplified models, which parameters should be known and to which accuracy they need to be known for realistic site-specific scenarios. These simplified models consequently suppress site-specific effects and concentrate on the parameters investigated.
To compare single parameters, other aspects of the model must be kept constant, even if this does not represent a real-world scenario. For instance, bottom-hole pressure, which, due to the fixed flow rate, depend solely on permeability, can exceed lithostatic pressure.
Parameter values against time to thermal breakthrough for
model experiments with homogenous and isotropic structure (Scenario 1).
Panels
In Scenario 1, we explore the role of porosity, permeability, orientation, and magnitude of the BHG on fluid flow and geothermal lifetime for a homogenous and isotropic reservoir volume (Fig. 1c). The times in which the HDI reaches the production well range from a few years only to a span of time that, in many cases, exceeds the modelled time limit (Fig. 2a–c).
Our results show that in the low-permeability models (10
The effect of the natural BHG on the modelled temperatures becomes apparent
if the shape of the HDI is examined (Fig. 2d–f). The HDI is (sub)spherical
in models with low and intermediate permeability and in models without BHG
(Fig. 2d). In models in which high permeability is combined with a BHG, the
HDI becomes ellipsoidal. In the latter cases, the ellipsoidal long
axis of the HDI is parallel to the BHG direction and its aspect ratio is controlled by
permeability and the magnitude of the BHG (Fig. 2e, f). The consequences of
the combination of high permeabilities with BHGs are, first, that the HDI
encloses a reduced narrower volume (Fig. 2e–f) and, second, that as a
consequence the chances of extreme cases occurring increases (in which the
HDI reaches the production well either very quickly or never at all; Fig. 2b, e, f). In other words, the higher the permeability of a reservoir is,
the more the development of the shape of the HDI is controlled by the BHG,
while the probability of the HDI reaching the production well decreases. For
instance, in models with permeabilities of 10
Our results show that the role of porosity is subordinate to the other
parameters (Fig. 2c). However, porosity still contributes to differences in
observed breakthrough times. In the case of the high permeability combined with
highest southwards-directed BHG, the breakthrough times vary by 5 years.
In the same model, with the magnitude of the BHG at only 1 mm m
In addition, in this scenario we tested the effect of the distance between
production- and injection wells on time to thermal breakthrough. We used the
model setup with
Time to thermal breakthrough vs. distance between injection
and production wells. The plot contains the results of 150 simulations. For
models without BHG, the relationship of time to thermal breakthrough to
distance is not linear. The increasing spread observed at the greater
distance is due to the influence of the BHG, which increases with distance.
The basic model setup is identical to the medium porosity and permeability
model (
In Scenario 2, we investigate the role of permeability contrasts in layered
reservoirs by carrying out three series of experiments with different
permeabilities (Fig. 1d). Since Scenario 1 showed that porosity is of minor
importance, we kept porosity constant and used the medium value for porosity
from Scenario 1 (14 %) in all Scenario 2 experiments. The permeabilities
of the reservoir layers in the three series were assigned values of
10
Parameter values against thermal breakthrough for model
experiments with layered permeability contrasts (Scenario 2). Panels
In the models in which the reservoir layers were assigned the lowest
permeability (10
In the models with intermediate permeabilities (10
In models with highly permeable reservoir layers (10
Parameter values against time to thermal breakthrough for
model experiments with vertically oriented fracture anisotropy (Scenario 3).
Panels
The development of the temperature field over time (Fig. 4j) is shown for
three model runs with different permeability contrasts using the model with
intermediate reservoir layer permeability (Fig. 4c, f, i). The temperature
drop at the production well depends on the permeability contrast between
reservoir and confining layers and is quicker with increasing permeability
contrast. In the model runs presented in Fig. 4j, temperatures stabilize
at a final temperature of about 100
In Scenario 3, we introduce permeability anisotropy. Permeability is
increased by 1 to 3 orders of magnitude in the vertical plane, compared to
other directions. This model scenario represents a vertically fractured
reservoir (Figs. 1e and 5). These models use the medium porosity (
We observe, in this series of models, times to thermal breakthrough that
range from less than 10 years to more than 200 years (Fig. 5a–c). This
range, however, is restricted to models with N–S-striking fracture
anisotropy, i.e. when the wells are aligned parallel to the direction of
high permeability. In the other cases, with the anisotropy oriented NE–SW,
NW–SE, or E–W, i.e. at an angle to the well configuration, the HDI does
not reach the production well in 200 years (Fig. 5a). This effect occurs for
fracture anisotropies of 1 order of magnitude, but at 10
Comparatively low permeability anisotropies of 10
In Scenario 4, we investigate the thermal development of a faulted
geothermal reservoir for two sub-scenarios (Fig. 1f). In the first
sub-scenario, the fault zone consists of a highly permeable damage zone
(10
Temperature development and shapes of the HDI for faults
that consist of a damage zone. In panels
For the first sub-scenario, the shape of the HDI is partly defined by the
damage zone and expands predominantly in the surroundings of the injection
well, taking an overall prolate shape (Fig. 6a–c). The temperature at the
production well stabilizes after about 10–20 years (Fig. 6d). The
100
Temperature development and shapes of the HDI for faults
that consist of a damage zone with a positive fault-parallel fracture
anisotropy. In panels
When modelling cases with a fault-parallel fracture anisotropy in the damage
zone (Fig. 7), for northwards-, eastwards-, southwards- and westwards-directed BHGs, the
channelling effect increases and the volume of the HDI, independent of the
orientation of the BHG, is restricted to the fault zone (Fig. 7a–c, e–f).
This channelling effect leads, in the case of fault-parallel BHGs, to a wide
spread of time-dependant temperature behaviour (Fig. 7d). For example, in
the case of the highest northwards-directed BHG, almost no temperature reduction
at the production well is observed. For the highest southwards-directed BHG,
the production temperature falls below the 100
For the eastwards- and westwards-directed BHGs, differences in the temperature development exist (Fig. 7g), in contrast to similar models without anisotropy (Fig. 6g). In these cases, BHGs oriented in the dip direction of the fault show a faster temperature drop compared to BHGs opposed to the dip direction.
Temperature development and shapes of the HDI for faults
that consist of an impermeable fault core surrounded by two damage zones. In
In the second sub-scenario, we increased the permeability of the damage zone
compared to the host by 2 orders of magnitude to 10
In the case without fault-parallel fracture anisotropy, the shapes of the HDIs are restricted on the eastern side by the impermeable fault core and extrude on the western side into the host rock (Fig. 8a–c, e–f). This bulge is concentrated around the injection well; otherwise, the channelling effect leads to a HDI that is largely defined by the high-permeability part of the western damage zone, in which both wells are placed. These observations are independent of the orientation of the BHG, i.e. parallel or normal to the strike of the fault.
The temperature development follows the same pattern as in the previous
model without fault core (Figs. 6, 8), and it is independent of the
orientation and magnitude of the BHG. It is, however, slightly quicker; the
range between the different northwards- and southwards-directed BHGs is smaller
and does not exist between the eastwards- and westwards-directed BHGs. Only for
the highest northwards-oriented BHG does the temperature stay above the
100
Temperature development and shape of the HDI for faults
consisting of a damage zone with fault-parallel fracture anisotropy and an
impermeable fault core. In
Introducing fault-parallel permeability anisotropy into the damage zone
(Fig. 9) has the effect that the HDI becomes restricted almost entirely to
the western damage zone, i.e. the part in which the wells are situated. In
the case in which a BHG is not applied (Fig. 9a), the HDI utilizes a large
part of the damage zone, restricted to the south by the production well.
Northwards-directed BHGs (Fig. 9b) produce a “fin”-like pattern within the
modelled domain, i.e. the HDI extends from the production well towards the
injection well along the damage zone. High southwards-directed BHGs (Fig. 9c), in contrast, result in a small oblate HDI confined between production
and injection wells. In terms of the temperature development (Fig. 9d),
these patterns reflect different behaviours. The highest northwards-directed
BHG almost entirely hinders a temperature drop at the production well. On
the contrary, the highest southwards-oriented BHG causes the production
temperature to fall below the 100
When testing this setup for westwards- and eastwards-directed BHGs, the production
temperatures reached the 100
Petrophysical properties, e.g. porosity and permeability, control the
quality of a geothermal reservoir. However, these properties may vary
significantly within a given volume. For instance, permeability is
frequently observed to vary over several orders of magnitude (Heap et al.,
2017; Kushnir, 2018; Manning and Ingebritsen, 1999); porosity may vary by 10
percent or more (e.g. Farrell et al., 2014; Heap et al., 2017; Kushnir,
2018; Zhang, 2013). The variability of these (Freudenthal, 1968; Krumbholz
et al., 2014a) and other petrophysical parameters (Alava et al., 2009;
Lobo-Guerrero and Vallejo, 2006) increases with scale. In addition, their
heterogeneous distribution and property values are often anisotropic in
terms of orientation, e.g. permeability caused by fractures often has a
preferred orientation (e.g. Laubach et al., 2004; Marrett et al., 2007;
Nelson, 1985; Watkins et al., 2018). To make a reliable prediction of
reservoir quality, it must first be determined to which accuracy these
parameters must be known (Bauer et al., 2017; Bauer, 2018). The ranges of
the parameter values we use in our modelling experiment for porosity,
permeability, and fracture anisotropy are, for example, typical for
sandstones in the Upper Rhine Graben (Germany; Fig. 10). Even in this
comparatively small area, the porosity is reported to cover a range from
close to zero to more than 25 % (Bär, 2012; Bauer et al., 2017; Jodocy
and Stober, 2011; Fig. 10a). The permeabilities determined for the same
reservoir rocks range from about 10
With our simplified models, we systematically investigate the effects and
the interplay of these important parameters on reservoir performance. In
addition, we have taken into account the effects of the BHG. Our experiments
do not aim to describe a specific reservoir model but rather to identify
prime parameters in terms of geothermal reservoir performance and the
accuracy to which they should be known. It was therefore important to keep
some model parameters constant. Thus, the use of model parameters was a
trade-off between values that lie in a realistic range and values that
allow for the comparison of the model results in the modelled time span. For this
reason, we decided to assign a relatively low temperature of 40
Rock volumes constitute in many cases, especially in sedimentary rocks, dual
porosity systems (Gringarten, 1984; Warren and Root, 1963) in which pore
space and fractures are fluid filled. Since pore fluid has a higher heat
capacity than rock (rock
The reason for these variations, and the predominantly subordinate role of
porosity, is, according to Scenario 1, provided by the interplay between
permeability and the BHG (Fig. 2a–c). If permeability is high enough, the
BHG controls shape, volume, and propagation direction of the HDI during heat
extraction. For permeabilities as low as 10
The importance of these findings is shown by cases such as the geothermal Hatchōbaru field in Japan (Bödvarsson and Tsang, 1982; DiPippo, 2005; Horne, 1982b). There, the injection and production wells were placed within a fault zone, resulting in good hydraulic connection. Moreover, the location of the wells was chosen in a way that the natural hydraulic background was oriented from the production to the injection well to avoid early thermal breakthrough. Nevertheless, the artificially introduced flow field was strong enough to outperform the BHG and the early drop in production temperature shows how fragile such high-permeability systems can be.
(Sub)horizontal permeability contrasts can be caused by layering in
sedimentary rocks and can span several orders of magnitude (Zhang, 2013),
even though these sealing properties are altered or reduced by barren
fractures. One example is clay layers that typically have permeabilities in
the range of 10
The greater part of permeability in a sedimentary rock volume is typically provided by fractures and their networks (e.g. Bear, 1993; De Marsily, 1986; Hestir and Long; 1990; Nelson, 1985). Thus, a thorough understanding and prediction of this reservoir property constitutes a major requirement when planning a geothermal reservoir. While microcracks are commonly predictable, (e.g. Kranz, 1983; Krumbholz et al., 2014b; Vollbrecht et al., 1994), making assumptions about fractures at decimetre and metre scales, i.e. the fractures that principally control fluid flow, is difficult (e.g. Bauer et al., 2017; Bauer, 2018; Laubach et al., 2004). When considering the cubic law, a single fracture, if it is wide enough, can control the fluid flow in a reservoir (e.g. De Marsily, 1986; Nelson, 1985; Odling et al., 1999). As a consequence, the prediction of fracture anisotropy at depth with the necessary accuracy is, at least, challenging and, at the most, impossible (e.g. Laubach et al., 2004; Ortega and Marrett, 2000; Watkins et al., 2018). Our models show that a fracture anisotropy of 1 order of magnitude (Fig. 5b) can channel the fluid flow so efficiently that the propagation of the HDI, in all other directions, is suppressed. If the anisotropy reaches just 2 orders of magnitude, which according to the literature (e.g. Bense and Person, 2006; Caine and Forster, 1999; Jourde et al., 2002; Watkins et al., 2018) must be considered to be a typical value, this suppression effect becomes saturated. In our models, even high BHGs cannot counteract this behaviour. According to our results, in this case, the BHG can only effect the reservoir lifetime when the BHG and fracture anisotropy are in line with the wells (Fig. 5a). The consequences are twofold: first, even comparatively low fracture anisotropy can hinder the establishment of a closed hydrothermal system; second, fracture anisotropy in the range of 1 order of magnitude, with respect to the bulk permeability, leads to either very short- or long-lived geothermal reservoirs, depending on the BHG properties and the orientation of fracture anisotropy (Fig. 5a, b, c).
Box-and-whisker plot of values reported for permeability
and porosity of Buntsandstein rocks from the Upper Rhine Graben.
The distance between production and injection wells is the only parameter known to any accuracy. It is inherent that increasing distance between production and injection wells has a positive effect on the lifetime of a geothermal reservoir. However, precise site-specific estimation of this effect requires in-depth knowledge of highly heterogeneous parameters, such as permeability and porosity. Given that both wells need to be hydraulically connected, the distance has a disproportionally high impact (Fig. 3), since the volume, between the wells, grows cubically. Our models suggest that the achievable lifetime does not necessarily scale directly with the volume, because the HDI is the result of the complex interaction between permeability contrast, fracture anisotropy, and the BHG. Moreover, increasing the distance between production and injection well also reduces the chance of establishing a closed system.
Faults were recently the focus of many studies of the economical
exploitation of geothermal energy. The main reason for this is that fault
damage zones promise significantly increased permeabilities (e.g. Bense et
al., 2013; Caine et al., 1996; Caine and Forster, 1999; Sibson, 1977) and
can provide positive temperature anomalies (Sanjuan et al., 2016; Vidal and
Genter, 2018). The typical characteristics of fault zones thus increase the
chance of high production rates of hot fluid, and this is potentially
further improved by fracture anisotropy within the damage zone, which is
often (sub)parallel to the fault (e.g. Bense et al., 2013; Caine et al.,
1996; Faulkner et al., 2010; Shipton and Cowie, 2003). However, a number of
critical studies exists (e.g. Bakhsh et al., 2016; Bauer et al., 2017;
Bauer, 2018; Biemans, 2014; Diaz et al., 2016; Loveless et al., 2014) that
discuss the risk and difficulties of exploring and exploiting fault zones as
geothermal reservoirs. The two main concerns reported are that, first, the architecture of a fault at reservoir depth is, due to the heterogeneous nature
of rocks and in particular that of the fault, difficult to predict,
i.e. exploration risk increases with complexity and heterogeneity of the
envisaged reservoir (e.g. Bauer, 2018; Bauer et al., 2018; Loveless et al.,
2014). The second concern is directly correlated to the expected high
permeability that makes a fault a prime target in geothermics. This is
because localized high permeabilities lead to channelling effects, i.e. the
geothermal reservoir potentially becomes restricted to the fault zone (e.g.
Biemans, 2014; Bakhsh et al., 2016; Moeck, 2014). Thus, the exploitation of
fault zones constitutes a trade-off between high permeability and reduced
reservoir volumes. Our simplified models support these findings and show
that faults, with damage zones that constitute positive permeability
contrasts of just 2 orders of magnitude, already exhibit these channelling
effects (Fig. 6). In these cases, the shape of the HDI is almost entirely
described by the extent of the damage zone. In most investigated cases, this
limitation of reservoir volume quickly leads to a sharp drop in production
temperature, i.e. in most configurations the temperature falls below the
100
However, the most promising configurations that allowed for longevity of fault-related reservoirs are those with a high fault-parallel BHG that leads directly from the production well to the injection well (e.g. Figs. 6b, d, 7b, d). Interestingly, for a BHG normal to the strike of the fault, we also observe different reservoir lifetimes as a consequence of differently shaped HDIs. We observed that, when the BHG is directed against the dip direction of a fault, the fault can be considered a more sustainable target for geothermal exploitation than a BHG oriented in the opposite direction (Figs. 7e, f, 8e, f). We argue that in the first case the BHG works against gravity in the fault zone, which slows the propagation of the HDI down, while in the opposing case, the BHG is supported by gravity and the progression of the HDI, and as a consequence the depletion of the reservoir is accelerated.
However, our models are still simplistic and the next steps of investigation should study how the channelling effect is altered as the permeability contrast between the fault zone and host rock increases, i.e. whether there is a transition zone of significant width between the low and high-permeability zones.
Another question that needs to be addressed when exploring fault-hosted or fractured reservoirs is the following – replenishment due to convective heat transport along the fault zone, as reported for numerous thermal anomalies in the Upper Rhine Graben (e.g. Sanjuan et al., 2016; Vidal and Genter, 2018). This point, often taken as an argument in favour of fault-related geothermal reservoirs, is not part of our study. Nevertheless, our results can help to constrain the observed channelling effects and therefore how high the replenishment rates in such reservoirs must be in order to counteract this.
We use over 1000 numerical experiments to systematically investigate
the effect of a number of parameters, e.g. permeability, and porosity, on the
potential lifetime of a geothermal reservoir. We varied the reservoir
parameters within realistic ranges and applied BHGs of different
orientations and magnitudes. From the results of our numerical sensitivity
study, we conclude the following:
Permeability, permeability heterogeneity, and fracture anisotropy
together with the BHG are the critical parameters that affect the lifetime
of a geothermal reservoir. While high permeability is an asset for the exploitation of geothermal
energy, our experiments demonstrate that it also comes with a risk. One the
one hand, high permeabilities are needed to generate sufficient flow rates.
On the other hand, high permeabilities in general, and in particular
localized high permeability, such as in layered sedimentary systems, in
fractures, and especially in fault damage zones, channel fluid flow and
strongly restrict the size of the geothermal reservoir that can be utilized. Typically, geothermal energy production aims to establish a closed system.
This is, according to our models, not trivial and depends strongly on
permeability, permeability heterogeneity, the internal structure of the
reservoir, and the BHG. This is especially true if the permeability is high
( Our models imply that, in many cases, the positive effect of porosity on
heat capacity and thus on the reservoir lifetime, is subsidiary, compared to
the effects of permeability and BHG; the impact of porosity decreases as
permeability increases. Due to the heterogeneous nature of rocks and fracture systems, it is, in
general, difficult to predict the lifetime of a geothermal system. This
holds especially true even if the required conditions for permeability are
met or exceeded and a BHG exists, because the BHG determines the shape and
propagation direction of the HDI. Therefore, the uncertainty in estimating
the lifetime inevitably increases.
Our results show that parameters, such as permeability and the BHG, can have
an unforeseeable large effect on the lifetime of a geothermal system. Thus, our
findings provide an important step forward in judging which parameters must
be known and to which degree they must be known to make site-specific models
as reliable and accurate as possible in the future.
All model results are presented in the article. Detailed results can be provided by the first author on request.
JFB and MK contributed equally to the article. The model experiments were designed by JFB, MK, and EL. Results were discussed by all authors. MK, JFB, EL, and DCT wrote the article. JFB, MK, and EL prepared the figures. All authors commented, read, and approved the final article.
The authors declare that they have no conflict of interest.
We thank our colleagues, Hans Ruppert, Klaus Wemmer, Jonas Kley, and Nicole Nolte for their support. We also thank Federico Rossetti, three anonymous reviewers, and Owen Callahan for their comments that helped improve our article.
This paper was edited by Federico Rossetti and reviewed by Owen Callahan and three anonymous referees.