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European Geothermal Congress 2022
Berlin, Germany | 17-21 October 2022
www.europeangeothermalcongress.eu
1
Impact of vertical layering and the uncertainty and anisotropy of hydraulic
conductivity on HT-ATES performance
Stijn Beernink1,2, Auke Barnhoorn1, Philip J. Vardon1, Martin Bloemendal1,2, Niels Hartog2
1 TU Delft, Faculty of Civil Engineering and Geosciences, Stevinweg 1 Delft
2 KWR Water Research Institute, Groningenhaven 7 Nieuwegein
s.t.w.beernink@tudelft.nl
Keywords: HT-ATES, hydraulic conductivity,
anisotropy, recovery efficiency, performance
ABSTRACT
The suitability of high temperature aquifer thermal
energy storage (HT-ATES) systems, among many other
applications in the subsurface, is for a large extent
determined by the hydrogeological aquifer properties.
Important subsurface properties that are challenging to
fully determine in the field are the hydraulic
conductivity, the vertical variation of hydraulic
conductivity and associated anisotropy factor between
vertical and horizontal hydraulic conductivity. To know
to what extend these uncertain parameters need to be
known for optimal design, the effect these properties
have on the performance of HT-ATES wells is studied
via numerical simulations of ATES wells under varying
operational conditions for yearly storage cycles.
Results show that for low temperature storage (<30 °C),
hydraulic conductivity anisotropy does not affect the
recovery efficiency, as energy losses driven by
buoyancy flow do not occur. For storage at high
temperature (90 °C), buoyancy flow negatively affects
recovery efficiencies, but it’s influence decreases with
lower vertical permeability (higher anisotropy). HT-
ATES wells in vertically layered aquifers are compared
to homogeneous aquifers with equal upscaled hydraulic
conductivity determined with averaging. When the
vertical layering variation occurs on a relatively large
scale, the systems perform differently (in most cases
more energy loss due to buoyancy flow and conduction,
in some cases positive influence due to re-use of
upward driven hot water.) Only when the layers are
small (m scale) and equally distributed across the
height of the aquifer, HT-ATES performance is similar
to equal homogeneous anisotropic scenario.
In general, the results of this study indicate that the
variability of hydraulic conductivity anisotropy and
layering in an aquifer impact HT-ATES performance.
Moreover, upscaling of initial hydraulic conductivity
for performance modelling is often not possible on the
aquifer scale. Hence, it is essential to perform
characterization of the aquifer on appropriate scales
(both small scale and large scale) and perform
modelling by using appropriately upscaled hydraulic
conductivity or by simulating the appropriate sub-
layers in the aquifer.
1. INTRODUCTION
Driven by the goal to reduce CO2 emission as soon as
possible (IEA, 2019), the energy transition from fossil
to renewable energy sources is accelerating. However,
renewable sources (e.g. geothermal, solar, wind) have a
mismatch in availability and demand of energy.
Therefore, a strong need for large scale storage methods
is present. For large scale storage of sensible heat, High
Temperature Aquifer Thermal Energy Storage (HT-
ATES) is regarded as one of the most promising
technologies to do so (Fleuchaus et al., 2018; Kallesøe
& Vangkilde-Pedersen, 2019).
Low temperature ATES (LT-ATES) systems (<30 °C)
are commonly applied and a proven technology, while
HT-ATES systems are applied occasionally as they
exhibit several key challenges. With HT-ATES
systems, heat is stored at higher temperatures (e.g. 30 –
100 °C) which makes it better applicable for integration
with e.g. district heating networks, geothermal and
solar energy. HT-ATES systems utilize aquifers in the
subsurface, using tube wells, to inject, store and recover
heated groundwater. In time of heat surplus (e.g.
summer, during the day), relatively cold groundwater is
extracted from the subsurface, heated by use of a heat
exchanger and subsequently stored in a different well.
After storage, the heated groundwater is extracted and
used in times of heat shortage (e.g. winter, during the
night). In the subsurface energy losses occur due to
movement of- and heat transfer from the stored body of
warm water. For successful operation of HT-ATES
systems, these energy losses should be minimized
(Fleuchaus et al., 2018).
For LT-ATES systems, conduction and dispersion
leads to energy losses (Bloemendal & Hartog, 2018).
Additionally for HT-ATES systems, energy losses due
to buoyancy flow (also often referred to as free
convection) can be of considerable impact on the
performance (Sheldon et al., 2021; van Lopik et al.,
Beernink et al. 2022
2
2016; Winterleitner et al., 2018). Buoyancy flow occurs
because of the density difference between the stored hot
(light) groundwater and the cold (dense) ambient
groundwater. This results in upward flow of the hot
water, away from the well at the top of the aquifer
(Figure 1). The buoyant force is determined by the
density difference between the hot water body injected
in the well and the ambient temperature. The aquifer
hydraulic conductivity then determines to what extend
this buoyant force leads to flow of groundwater. The
hydraulic conductivity is determined by the local
temperature (viscosity of water decreases with
increasing temperature) and the intrinsic permeability
of the aquifer (Hellström et al., 1988). The convective
cell that develops due to the buoyant force is influenced
by the aquifer thickness – for larger aquifer thickness
also a larger convective cell develops and the warm
water flows further away from the well at the top
(Hellström et al., 1988).
Determination of appropriate initial aquifer vertical and
horizontal hydraulic conductivity on an aquifer scale is
challenging (Nordahl & Ringrose, 2008). Hydrological
test can be used to determine the field scale horizontal
and vertical hydraulic conductivity (e.g. by pumping,
injection, slug test), but these are often very expensive
and may not give the resolution necessary (Parr et al.,
1983).
As a result, available information is often limited (e.g.
horizontal hydraulic conductivity but not vertical) or
data is only available on a relatively small scale
(intrinsic sediment property from core analysis). For
design, property values are usually chosen on the
aquifer scale to simulate HT-ATES performance.
However, it is unclear to what extent and under which
conditions it is possible to upscale hydrogeological
properties to identify homogeneous aquifer scale
conditions and if so, how variations in these properties
should be combined properly for representative
representation of the subsurface conditions.
Therefore, in this study the effect of initial hydraulic
conductivity and anisotropy variation on buoyancy
flow losses is investigated. Moreover, the influence of
vertical layering in aquifers is quantified and assessed
if upscaled hydrogeological properties, using analytical
averaging methods, result in similar performance. To
this end, we use the SEAWAT model to simulate the
performance of HT-ATES systems for varying
hydrogeological and storage conditions. These results
aim to give insights in the impact of subsurface data
uncertainty on HT-ATES performance, and thus
leading to insights to optimize HT-ATES.
Figure 1: Schematic sideview of a single HT-ATES
well that is influenced by buoyancy driven
flow.
2. THEORY: HYDRAULIC CONDUCTIVITY
AND ANISOTROPY
The hydraulic conductivity (or often referred to as
permeability) is used to identify the ability of a porous
medium to allow flow through it for a specific fluid.
The hydraulic conductivity is determined by the
intrinsic permeability and the characteristics of the fluid
travelling trough it.
g
K
=
(1)
Where K is the hydraulic conductivity (m/s), κ the
intrinsic permeability (m2), ρ the density of the fluid
(kg/m3), g the gravitational constant (9.81 m/s2), and μ
the viscosity (kg/m*s). As ρ and μ decrease with
increasing temperature, the hydraulic conductivity
changes with temperature. In this study, the
ambient/initial hydraulic conductivity for the initial
groundwater characteristics is defined as Tamb=12,
fresh water,
The intrinsic permeability is determined by the
connectivity between the effective pores in the
medium. On the grain size scale, the depositional
history and type of sediments determines the
permeability (K) and anisotropy (Fani) of the sediment
(Figure 2). The vertical anisotropy factor is the ratio
between the horizontal and the vertical K:
h
ani
v
K
fK
=
(2)
Due to compaction and deposition conditions, Kv is
usually smaller than Kh, which occurs because grains
are not perfectly round and due to the structure
occurring due to deposition and in situ stresses (Figure
2). Moreover, after deposition the burial of sediments
under increasing pressures can increase the anisotropy.
The initial anisotropy ratio of sand grains, for typical
packing pressure and grain shape, is between 2-3 (Lake,
1988; Meyer & Krause, 2006). However, when the
anisotropy is measured on the core scale to aquifer
scale, the anisotropy factor can increase up to a factor
10 to 100 (Lake, 1988; Xynogalou, 2015). This occurs
because it is more likely that different
Beernink et al. 2022
3
sediments/lithotypes (present due to aquifer
heterogeneity) are cut across when the scale is enlarged
(Burger & Belitz, 1997; Huysmans et al., 2008). Hence,
in general, the anisotropy that is measured is dependent
on the scale of the measurement and increases with
increasing scale.
Figure 2: Schematic overview of the difference
between isotropic and anisotropic sediments.
2.1 Upscaling hydrogeological properties
Because of lacking subsurface data and computational
power, hydrogeological properties on the grain size
(sub-cm) scale are not used for modelling studies on
groundwater and heat flow systems like HT-ATES
(100m+ scale). Therefore, these small scale
measurements often need to be upscaled to match the
size of the grids of the simulator that is used. It is
however not straightforward to do so (Nordahl &
Ringrose, 2008; Wen & Gómez-Hernández, 1996).
In general, additive properties like porosity are easily
upscaled, using simple averaging methods. Non-
additive properties like permeability, which are
dependent on their relative location and connectivity to
their surroundings, are not easily upscaled (Nordahl &
Ringrose, 2008). The Representative Elementary
Volume (REV) theory provides information on the
volume that must be used to accurately calculate the
representative upscaled value of the hydrogeological
property (Bear, 1972). The size of the REV is
determined by the spatial variability of the property and
problem considered. When the sediment is more
heterogeneous, a relatively larger volume is needed to
calculate a representative upscaled value. However, for
stratified media without lateral heterogeneity exact
solutions exists that can be used to determine an
upscaled value for the vertical hydraulic conductivity
(de Marsily et al., 2005). Following the approach of de
Marsily et al. (2005), the harmonic mean is used to
upscale the vertical hydraulic conductivity:
1
()
()
()
vn
iv
H tot
KHi
Ki
=
=
(3)
where H(tot) is the aquifer thickness, H(i) is the
thickness of the, layer considered and i is the layer
number of the n number of layers identified. For the
horizontal hydraulic conductivity, the arithmetic mean
(normal average) is used:
1
( ) ( )
()
nh
hi
K i H i
KH tot
=
=
(4)
Often, the aquifers used for storage and recovery
systems like HT-ATES and ASR are schematized as a
horizontally stratified medium. Thus the harmonic and
arithmetic mean are potentially useful for upscaling of
measured hydraulic conductivity in the aquifer.
2.2 Determination of hydraulic conductivity in
practice
The horizontal hydraulic conductivity of the aquifer is
of high interest, as this determines the capacity of
injecting and extracting groundwater from the aquifer,
defined as the specific flow rate per meter of well
screen. This can be estimated by analysis of the grain
size distribution on a sub-meter scale (Wang et al.,
2017) and/or by use of hydraulic testing on the aquifer
scale (Kruseman et al., 1970). Moreover, the hydraulic
conductivity on ~meter scale can be assessed by use of
coring analysis. In addition, innovative logging tools
like Nuclear Magnetic Resonance (NMR) can be used
to determine porosity and hydraulic conductivity in the
near vicinity of the borehole at ~meter scale (Knight et
al., 2016)
The vertical hydraulic conductivity is of interest for
systems where vertical flow is of importance, like HT-
ATES and aquifer storage and recovery (ASR) systems.
This property is more difficult to measure, but core
analysis (~meter scale) and specific pumping tests
using partially penetrating wells (aquifer scale) are
available to determine this (Maliva, 2016).
In practice, uncertainties are present regarding the
quality, accuracy and data density of the
hydrogeological properties of lithofacies . Logging data
from a recently drilled well near Delft shows us that
inside an aquifer, a considerable degree of variability
exists. As shown in Figure 3, we observe an aquifer
between 150 to 185m depth. The variability in the GR
signal could indicate variation in sediment type (e.g.
sand versus silt and clay). It is thus of interest how these
variabilities would impact the hydraulic conductivity
and if a representative hydraulic conductivity can be
determined for the entire aquifer. In this study, we
compare scenarios with vertical variability (layering) to
homogeneous scenarios with equal (upscaled)
hydraulic conductivity and assess how upscaled
hydrogeological values compare to their homogeneous
match.
Beernink et al. 2022
4
Figure 3: Vertical variability in a Gamma Ray (GR)
signal of an example location near Delft at a
depth of 100 to 200m depth. A fixed GR value
is used to approximately delineate between
sand (yellow, low GR) or clay (grey, high GR)
3. METHODS
3.1 SEAWAT: density and viscosity dependent
groundwater modelling
The SEAWATv4 model, combines the groundwater
model MODFLOW (Harbaugh et al., 2000) and the
multi-species model MT3DMS (Zheng & Wang,
1999). This model is used to simulate viscosity and
density dependent heat and groundwater flow under
axisymmetric conditions (Langevin, 2008;
Vandenbohede et al., 2014). FloPy is used to control
and process the SEAWAT model from a python
environment (Bakker et al., 2016). Water viscosity
varies non-linearly with temperature (e.g. Voss (1984)).
The SEAWAT executable was adjusted, similarly to
van Lopik et al. (2016), to allow automatic non-linear
density variation with temperature.
The following conceptual modelling principles are
applied to define the model:
- Ambient groundwater is stagnant (no flow)
and 12 °C
- Yearly storage and recovery cycle
o Injection: 5 months
o Storage: 1 month
o Extraction 5 months
o Inactive: 1 month
- Injection volume is equal to extraction volume
- Fully penetrating well screens
- Flow is divided over aquifer according to
relative horizontal hydraulic conductivity of
each cell
- Thermal conductivity and longitudinal/
transversal dispersion is equal for all
simulations
The geohydrological and thermal properties that are
used are given in Table 1.
The boundary conditions at the top and bottom of the
model were set to zero flow and constant temperature.
At the sides of the model constant head and constant
temperature apply.
3.2. Assessment framework
The performance of the HT-ATES wells was calculated
as the recovery efficiency, the yearly amount of energy
that is recovered (Erecovered) after storage divided by the
total injected amount of energy (Einjected):
cov ()
()
rec rec amb w
re ered
th
injected inj inj amb w
V T T c
E
E V T T c
−
==
−
(4)
Where Vrec and Vinj is the yearly recovered and injected
volume (m3), Trec and Tinj the recovered and injected
average temperature (°C), Tamb the ambient
groundwater temperature (12 °C in this study) and cw
the volumetric heat capacity of water (J/kg/m3).
Table 1: Geohydrological and thermal properties
used for the SEAWAT model used in this
study (Bloemendal & Hartog, 2018; Caljé,
2010)
Parameter
Value
Porosity
0.3
Longitudinal dispersion
0.5 m
Transversal dispersion
0.05 m
Density water at 0°C
1000 kg/m3
Density solids
2640 kg/m3
Specific heat capacity solid
710 J/kg °C
Specific heat capacity water
4183 J/kg °C
Thermal distribution coefficient
(retardation)
0.00017
m3/kg
Thermal conductivity of aquifer
2 W/m °C
Thermal conductivity of aquitard
2 W/m °C
Thermal conductivity water
0.58 W/m °C
Bulk thermal conductivity
0.10837
m2/day
3.3 Scenarios
Horizontal hydraulic conductivity can vary widely for
different types of unconsolidated sediments (Bot,
2011), with the range of values for different sediment
types typically being in the following ranges:
- Sand: 1 – 100 m/d
- Silt: 0.05 – 1 m/d
- Clay: 0.0001 – 0.05 m/d
For this study, a base case homogeneous isotropic
conceptual aquifer model of medium grained sand is
constructed, with a horizontal hydraulic conductivity
(Kh) of 5.5 m/d and vertical hydraulic conductivity (Kv)
of 5.5 m/d with an aquifer thickness of 60m. For all
simulations, a 60m thick, fully screened, aquifer is used
(Figure 4A). Subsequently, the anisotropy factor of the
homogeneous aquifer is varied with a factor 3, 10 and
27 (Figure 4A), which represents the broad range of
observed anisotropies in practice and previous studies
(Lake, 1988; Xynogalou, 2015).
Finally, vertical layering is introduced in the aquifer
model. Four different layering scenarios are made. The
K values are chosen such that the average upscaled
Beernink et al. 2022
5
values match the homogeneous aquifer, using equations
(3) and (4) to calculate the average K. This is modelled
for the Fani=3 scenario (Figure 4B) and the Fani=27
scenario (Figure 4C). This results in isotropic layers
(Kh=Kv) of 10 or 1 m/d for Fani=3 and isotropic layers
of 10.9 or 0.1 m/d for the Fani=27 scenario. Please note,
the sub-layers of the layered scenarios are isotropic, but
the upscaled (averaged) aquifer scale hydraulic
conductivity is equal to the homogeneous scenarios.
The Fani=3 variants can be seen as a variation of
medium grained sand (10 m/d) and fine sand/silt (1
m/d) layers). For Fani=27, the difference in hydraulic
conductivity is representative for medium grained sand
and silt/clayey layers.
In scenario 1 (equal for both Fani=3 and Fani=27), three
layers of higher hydraulic conductivity and three layers
of lower hydraulic conductivity are equally distributed
over the aquifer. In scenario 2, the high hydraulic
conductivity layer is found in the top 30m of the aquifer
and the low conductivity layer in the bottom part. For
scenario 3, the opposite applies. For scenario 4, the
aquifer is distributed in 1m thick layers, 30 layers of
high conductivity and 30 layers of low conductivity are
equally distributed over the total aquifer thickness.
Operational conditions variation
Operational conditions were varied as follows: storage
volumes of 100,000 m3 or 1,000,000 m3 and storage
temperatures of 30°C or 90°C (representing LT-ATES
and HT-ATES, respectively), meaning that 4
simulations are performed for each aquifer model
(Table 2).
Table 2: Varied storage conditions for all model
simulations in this study
Figure 4: The modelled scenarios in this study. A) the homogeneous isotropic base case scenario
and scenarios with anisotropy ratios (F_ani) of 3, 10 and 27. In the bottom, four vertically
layered (heterogeneous) aquifers with equal average hydraulic conductivity with B)
anisotropy factor = 3 and C) anisotropy factor = 27. Upscaled Kh is calculated using the
arithmetic mean (eq. 4), upscaled Kv is calculated using the harmonic mean (eq. 3).
4. RESULTS AND DISCUSSION
4.1 Homogeneous scenario
The simulated hot well temperature for the base case
(homogeneous isotropic aquifer) is shown in Figure
5A, including the temperature and storage volume
variations. Figure 5B shows the temperatures at the end
of the hot water injection in the 5th year. For a storage
volume of 105 m3 per year a thermal radius develops of
~30m, for the large storage volume (106 m3 per year)
the thermal radius is about 80m (Figure 5B).
During injection, the temperature of the HT-ATES well
is equal to the injection temperature and decreases
during storage and extraction (Figure 5A). However,
with each cycle, the minimum well temperature
increases and the recovery efficiency thus increases
with each cycle over time (Figure 6). The highest
A)
Kh Kv Kh Kv Kh Kv Kh Kv
B) C)
Kh Kv Kh Kv Kh Kv Kh Kv Kh Kv Kh Kv Kh Kv Kh Kv
10m 10 10 10 10 1 1 10.9 10.9 10.9 10.9 0.1 0.1
10m 1 1 10 10 1 1 0.1 0.1 10.9 10. 9 0.1 0.1
10m 10 10 10 10 1 1 10.9 10.9 10.9 10.9 0. 1 0.1
10m 1 1 1 1 10 10 0.1 0.1 0.1 0.1 10.9 10.9
10m 10 10 1 1 10 10 10.9 10.9 0.1 0.1 10.9 10.9
10m 1 1 1 1 10 10 0.1 0.1 0.1 0.1 10.9 10.9
5.5 1.82 5.5 1.82 5.5 1.82 5.5 1.82 Average 5.5 0.2 5.5 0.2 5.5 0.2 5.5 0.2
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 1
<- 60m ->
Scenario 2
Scenario 3
Scenario 4
Base Case
F_ani = 3
F_ani = 10
F_ani = 27
5.5
5.5
5.5
1.82
5.5
0.55
5.5
0.2
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
10 10
1 1
Storage temperature
(°C)
Yearly storage
volume (m3)
1
Tinj = 30
Vinj = 105 m3
2
Tinj = 30
Vinj = 106 m3
3
Tinj = 90
Vinj =105 m3
4
Tinj = 90
Vinj =106 m3
Beernink et al. 2022
6
recovery efficiency is observed for the 30 °C scenario
with large storage volume. The lowest recovery
efficiency is observed for the 90 °C scenario with low
storage volume. In general, the recovery efficiency is
higher for low storage temperature and large storage
volume.
For the 30 °C variants, the thermal front is seen to have
a slight angle with respect to vertical due to the small
density difference (Figure 5B). For the 90 °C variants,
strong tilting is observed at the thermal front due to
buoyancy driven flow. At the top of the aquifer, the
stored hot water drifts away from the well screen more
than 2x the thermal radius, and cannot be recovered
during extraction (Figure 5B), explaining the reduction
in recovery efficiency. The impact of the buoyancy
flow losses (difference between 30 and 90 °C scenario)
on the recovery efficiency of heat is more than 30% for
the relatively small storage volume (105 m3) and about
10% for the relatively large storage volume (106 m3).
Figure 5: The Base Case homogeneous modelling results. A) the well temperature during 5 years of
simulation for the four modelled scenarios. B) cross section view of the temperature
distribution in the aquifer at full injection volume in the 5th year of operation for the four
scenarios.
Figure 6: Recovery efficiency increases with
number of years for the homogeneous base
case aquifer model.
4.2 Anisotropy variation of homogeneous aquifer
Figure 7 shows the results of different anisotropy
factors of the homogeneous base case scenario. Our
simulations show that the 30 °C variants are insensitive
to the anisotropy factor. For the 90 °C variants, higher
anisotropy factors (Kh/Kv), lead to considerably higher
recovery efficiencies during the 5th cycle. For the large
storage volume we observe an increase of ~10%
recovery efficiency and especially for the relatively
small storage volume the performance increases
considerably (>35% increase between anisotropy factor
1 - 27). With an anisotropy factor of 27 (Kv=0.2 m/d),
the 30 and 90 °C variants have nearly equal
performance, meaning that the effect of buoyancy flow
is decreased strongly. The recovery efficiency increases
with higher anisotropy factors and shows a non-linear
progression with biggest changes at small anisotropy
factor (e.g. 1 to 3).
Beernink et al. 2022
7
For systems that are prone to buoyancy flow losses, it
is thus of high importance to accurately determine the
representative vertical hydraulic conductivity of the
aquifer, relative to the horizontal hydraulic
conductivity. Here we use an aquifer with a medium
horizontal hydraulic conductivity (Kh=5.5 m/d); for
aquifers with higher horizontal hydraulic conductivity
(e.g. 10 - 100 m/d for coarse grained sand aquifers), the
anisotropy factor could be the difference between a
suitable and an unsuitable aquifer for HT-ATES
systems.
Figure 7: The recovery efficiency in the 5th year at
increasing anisotropy factor (1, 3, 10, 27) for
the four modelled operational conditions.
4.3 The effect of upscaling by averaging of vertically
layered aquifers
The impact of upscaling hydraulic conductivity by
averaging (equation 1 and 2) of vertical layers is
explored in this section for the 90°C simulations. For
all scenarios, the upscaled aquifer scale Kv and Kh is
equal (calculated equation 3 and 4). Figure 8 presents
the recovery efficiency in the 5th year for the various
layered scenarios (bar 2-5). All results are compared to
their equal homogeneous anisotropic scenario (first bar
in figures) and the isotropic base case scenario
(horizontal line).
As shown in Figure 8A, for Fani =3 and a storage
volume of 100,000 m3, the homogeneous scenario has
a recovery efficiency of 0.53. The recovery efficiency
increases for layering scenarios 1 (+0.02) and 3 (+0.17).
Layering scenario 2 has a lower relative performance (-
0.07). Layering scenario 4, where the aquifer is divided
into equally distributed 1m thick layers of higher and
relatively lower hydraulic conductivity, shows equal
performance to the homogeneous scenario and heat
distribution in the aquifer is also very similar (Figure
9).
As shown in Figure 8C, when the storage volume is
increased to 1,000,000 m3 with F_ani=3, the recovery
efficiency of the homogeneous scenario is 0.78 (Figure
8C). The performance for the layered scenarios is again
similar – performance for scenario 1 (0.77) and 4 (0.78)
is similar, lower recovery efficiency is found for
scenario 2 (-0.08) and the recovery efficiency increases
for scenario 3 (+0.1).
The effect of layering is different when the hydraulic
conductivity of the low permeability layers is decreased
more, resulting in an anisotropy factor (F_ani) of 27
(Figure 8B an 8D). For a storage volume of 100,000 m3,
the recovery efficiency of the homogeneous scenario is
0.78 (Figure 8B). Again, layering scenario 4 (1m
equally distributed layers) has equal recovery
efficiency (0.78). The other layering scenarios have a
negative effect on the performance (scenario 2 = -0.07,
scenario 3 = -0.35, scenario 4 = -0.21).
As shown in Figure 8D, when the storage volume is
increased to 1,000,000 m3, the homogeneous scenario
has a recovery efficiency of 0.86. Here, the same
observations are made: scenario 1-3 have lower
recovery efficiency (-0.03, -0.12, -0.06 respectively)
and the performance of scenario 4 is very similar to the
homogeneous scenario.
For all simulated variants, scenario 4, where the
hydraulic conductivity is distributed equally per 1m
aquifer thickness, gives similar results for all variants
(recovery efficiency, visually) to the homogeneous
anisotropic aquifer simulation (Figure 8, Figure 9). This
is similar to findings of Ward et al. (2008) where they
assessed the anisotropy due to layering for ASR
systems. Hence, when the stratification thickness is
small enough and equally distributed over the aquifer,
analytical averaging and upscaling is appropriate to
simulate the performance of aquifer storage systems.
Layering scenario 2 leads in all cases to lower recovery
efficiencies. Here, most volume is stored in the upper
part of the aquifer. As this layer has relatively high
hydraulic conductivity (Kh=10, Kv=10 versus Kh=5.5,
Kv=1.82) buoyancy flow is stronger. Although the layer
where buoyancy flow occurs is only 30m thick, this
leads to more energy losses compared to the buoyancy
flow occurring in the 60m thick anisotropic
homogeneous simulation. Also, when the water is not
equally injected into the aquifer, a larger contact area
(m2) exists between the hot and ambient groundwater,
meaning that losses due to conduction also increase
(Bloemendal & Hartog, 2018). The same occurs for
layering scenario 3, only here most water is injected
into the bottom of the aquifer. For the Fani=3 scenario,
this leads to strong upward flow into the less permeable
layer above (Figure 9). This ‘lost’ hot water is
subsequently reused when water is extracted, leading to
an increase in recovery efficiency. For Fani=27, this
does not occur anymore because the hydraulic
conductivity in the upper lower is too low for the
upward flow and recovery of hot water in this layer.
In general, the following is observed:
- If the layering is distributed equally and in
small steps (scenario 4), analytical averaging
for homogeneous simulations is appropriate as
this leads to equal HT-ATES performance.
Beernink et al. 2022
8
- If the layering is distributed non-uniformly
and in relatively big parts (scenarios 1, 2, 3),
the simple averaged Kh and Kv is not
representative. This means that other methods
for upscaling are needed or that it is needed to
model the HT-ATES system as a layered
systems with separate lithofacies instead of
one homogeneous aquifer.
Figure 8: The recovery efficiency in the 5th year of operation for the vertically layered scenarios
(scenarios 1 – 4) compared to their equal homogeneous anisotropic variant (Homoge) for
Tinj=90 °C.
Beernink et al. 2022
9
Figure 9: Sideview of the 90 °C scenarios for 100,000 m3/year storage volume with layered hydraulic
conductivity. Top: F_ani = 3, bottom: F_ani=27 (layering of scenarios is shown in Figure 4B
and 4C).
5. CONCLUSIONS
Numerical simulations of HT-ATES wells under
varying storage conditions are carried out to investigate
the effect of varying intrinsic permeability, anisotropy
and vertical hydraulic conductivity layering.
The main conclusions are summarized below:
- At 30°C storage temperature, losses due to
buoyancy flow are insignificant, at 90°C
storage temperature, buoyancy flow losses can
be of large impact. For the latter, losses due to
buoyancy flow decrease with decreasing Kv
(increasing anisotropy).
- Upscaling of hydraulic conductivity in
vertically layered aquifers by averaging
methods is not applicable when the layers are
distributed unequally and vary on a relatively
large scale (>m scale).
- For vertically stratified aquifers with
relatively small scale (m scale or smaller) and
equally distributed layers, results are equal to
homogeneous simulations and analytical
averaging is thus appropriate for upscaling.
These simulations show us the importance of
determination of horizontal and vertical hydraulic
conductivity for HT-ATES performance on the
appropriate scale. In general it is not possible to upscale
the >1 meter scale hydraulic conductivity variability.
Appropriate upscaling for smaller lithofacies inside an
aquifer must be considered, meaning that an aquifer in
some cases cannot be represented as a homogeneous
unit but must be subdivided into multiple units for
modelling. Hence, for HT-ATES, aquifer
characterization methods and techniques are needed
that are able to determine the division of the aquifer in
appropriate sub-units at a >1 m scale, together with the
representative hydrogeological properties of these sub-
units.
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