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Stratabound Rayleigh convection observed in a 4Dhydrothermal reactive transport model based on theregional geological evolution of Allermohe (Germany)
M. KUHN1 ,* AND A. GUNTHER2 ,�
1TU Hamburg-Harburg, Water Management and Water Supply, Hamburg, Germany; 2TU Braunschweig, Department of
Environmental Geology, Braunschweig, Germany
ABSTRACT
We investigated stratabound Rayleigh convection as a means of transport for leaching of solutes from salt diapirs,
their dissipation into the Rhaetian sandstone aquifer and subsequent precipitation of anhydrite with resulting
cementation. Reactive transport modelling has been conducted in the context of the recent structure of the Aller-
mohe site and its palaeogeological development. Resulting flow fields depict large (km-scale) stratabound Ray-
leigh convection. However, our simulations show the vicinity of the Allermohe well as a potential area of
anhydrite dissolution in contrast to field observations, with precipitation concentrated elsewhere.
Key words: Allermohe, hydrochemical modelling, numerical modelling, palaeohydrology, SHEMAT, solute
transport, structural geological modelling
Received 29 September 2005; accepted 16 January 2007
Corresponding author: Michael Kuhn, RWTH Aachen University, Applied Geophysics, Lochnerstrasse 4–20, 52056
Aachen, Germany.
Email: [email protected]. Tel: +49 241 80 94831. Fax: +49 241 80 92132.
Geofluids (2007) 7, 301–312
INTRODUCTION
The Allermohe, well located south-east of Hamburg, Ger-
many (Fig. 1), was recently considered for the installation
of a major geothermal heating station (GHS). The target
aquifer for hot water was the Rhaetian sandstone, which
has fed the GHS of Neustadt-Glewe (100 km east of Ham-
burg) with up to 120 m3 of water per hour since 1995.
To reach the Rhaetian sandstone, the depth of the Aller-
mohe, 1 bore was increased to 3300 m in 1997, so that it
now taps a 70-m-thick sandstone aquifer with a tempera-
ture of 125�C. Although the temperature and thickness of
the aquifer are ideal for geothermal energy production, the
porosity, originally as high as 20%, is now largely occluded
by secondary anhydrite cement. As a result, the extractable
amount determined by a pumping test in 1998 is only
3 m3 h)1, and is too low for an economical use of the
resource (Baermann et al. 2000).
It is clear that the thermal environment is affected by
the presence of salt domes, and that the temperature field
is strongly coupled to the groundwater flow field as well as
to chemical reactions of salt dissolution. It is therefore use-
ful to investigate the interplay between those processes to
test conceptual hypotheses concerning anhydrite cementa-
tion. Intense research has been conducted in the past two
decades on fluid flow, heat transfer and mechanisms of salt
transport in aqueous solution.
The starting point for many of these investigations has
been the work of Hanor (1987), who presented geochemi-
cal and physical evidence for the existence of density inver-
sions in the Gulf of Mexico Coast pore fluids driven by
large-scale convective fluid flow with flow rates greater
than 1 m day)1. Hanor (1987) qualifies this conclusion by
noting that this fluid overturn must take place along a net-
work of interconnected sands because it is otherwise not
possible to drive large volumes of fluid at high velocity
across the existing shale beds.
*Present address: RWTH Aachen University, Applied Geophysics,
Lochnerstrasse 4–20, 52056 Aachen, Germany.
�Present address: Federal Institute for Geosciences and Natural
Resources, Stilleweg 2, 30655 Hannover, Germany.
Geofluids (2007) 7, 301–312 doi:10.1111/j.1468-8123.2007.00182.x
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd
Sharp et al. (2001) also studied the Gulf of Mexico
basin, a region penetrated by thousands of boreholes that
have produced extensive data sets, to resolve the question
of how observed high levels of sediment diagenesis can
occur in basins dominated by low-permeability shales. It
has been shown by Sharp et al. (2001) that diffusive trans-
port of diagenetic reactants cannot account for required
mass fluxes but that density-driven free convection can. As
shown by Bjorlykke et al. (1988), low-permeability argilla-
ceous strata in basins may retard or prevent such convec-
tion. In contrast, Sharp et al. (2001) support the concept
of free convection in the vicinity of salt domes. They have
shown that cross-formational solute transport due to con-
vection is feasible in areas with relatively thin shale layers
possessing permeabilities at the upper end of the expected
range of shale hydraulic conductivities, and can explain
field-based observations of salinity inversions. In their
study, heterogeneity in shale permeability was modelled as
conduits to enhance the potential for free convection. Wil-
liams & Ranganathan (1994) also applied conduits with
high vertical permeabilities of 10)14 m2, in combination
with simulation of dewatering processes, to explain thermal
anomalies around salt structures. Their simulations show
that the absence of conduits with sufficiently high vertical
permeability precludes the formation of thermal plumes
due to convection. However, they admit that there is no
knowledge on how wide, deep and permeable such con-
duits are or even how common or uncommon they might
be. Moreover, in regions with laterally extensive interbed-
ded shales and sands, the prerequisites formulated by Wil-
liams & Ranganathan (1994) may be difficult to satisfy.
Evans et al. (1991) point out that in salt dome environ-
ments groundwater is driven largely by density gradients
rather than by hydraulic head gradients. Those density gra-
dients arise from thermal effects due to the high thermal
conductivity of the salt relative to the surrounding rock,
and from varying salinities, due to dissolution of the salt
itself. Thermally driven convection near salt domes presents
a simple and plausible transport mechanism provided the
thermal effects are not overwhelmed by salinity effects
(Evans & Nunn 1989). The numerical model of Evans
et al. (1991) was able to predict upward flow, needed to
explain salinity inversion around salt structures in the Gulf
of Mexico, as shown by Hanor (1987), only when regional
groundwater salinity was relatively homogeneous and high.
The modelling approach presented in this study focused
solely on the Rhaetian aquifers without directly including
the adjacent strata because: (1) Allermohe region is charac-
terized by massive shales with thickness of up to 1000 m
both above and below the Rhaetian aquifers; (2) detailed
information about water composition and rock properties
are scarce at these depths; (3) convection is likely to have
been able to proceed without inputs from or outputs to
the adjacent shales; and (4) there is little definitive evi-
dence for the existence of fluid conduits that would have
allowed cross-formational flow. Although the conceptual
model is simple, the structural and numerical model is
sophisticated. The intention of the 4D numerical studies
(3D spatial and a geological structure-evolution through
time) using the simulation programme SHEMAT (Bartels
et al. 2003) is to:
• present a new technique of loose coupling between
structural geology and reactive transport modelling to
create a 4D numerical model taking into account chan-
ging topographic boundaries over geological time scales;
• emphasize the probability of stratabound Rayleigh con-
vection, without cross-formational flow, in structures
with strong relief close to salt domes;
• assess the hypothesis of Lenz et al. (1997), with regard
to stratabound Rayleigh convection, that the cementa-
tion of the Rhaetian reservoir is a result of leaching of
solutes from the neighbouring salt domes and subse-
quent precipitation of anhydrite.
Previous numerical simulations of circulation around salt
domes were two-dimensional (2D). We have developed a
3D model because 2D simulations of the Allermohe site
are not able to represent the flow field and temperature
distribution accurately. The geometry around the Aller-
mohe Well, in the vicinity of two salt structures, is too
complex to be approximated in 2D. Unlike previous stud-
ies, chemical reactions are implemented not only via trans-
port boundary conditions that reflect NaCl dissolution and
precipitation, but through a chemical module in SHEMAT
specifically designed for the numerical solution of mineral
reactions in highly saline solutions (Kuhn 2003).
4000
3500
3500
300025
00
2000
3500
MeckelfeldDiapir
AW
Cross-Section 1
Cross-Section 2
Cross-
Section 3
Cross-Section 4
ReitbrookDiapir
53°30' N10°00' E
53°24' N10°10' E
Lowermost CretaceousUpper JurassicMiddle JurassicPemian Salt
Major Normal FaultSyncline AxisAnticline AxisBoundary of Salt Domes
3 km
Fig. 1. Geological subcrop map (Lower Cretaceous and younger units
uncovered) of the study area (TK 2526, sheet Allermohe, Ehlers 1993,
modified after Baldschuhn et al. 2001). Isolines: depth contours of base of
Keuper horizon (b.s.l.). Also shown: locations of cross-sections and position
of the Allermohe well (AW).
302 M. KUHN & A. GUNTHER
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
GEOLOGICAL SETTING AND HISTORY
The study site is located SE of Hamburg (Germany)
between 53�24¢–53�30¢N and 10�00¢–10�10¢E (Fig. 1).
The study area is concurrent with part no. 2526 of the
geological map of Hamburg (Allermohe sheet, 1:25,000;
Ehlers 1993). The Allermohe well has been drilled at the
position 53�28¢N and 10�06¢E in the centre of the NE
quadrant of the map sheet (Fig. 1).
More than 100 deep boreholes have been drilled within
the area of Allermohe during hydrocarbon and iron ore
exploration. As a result, the subsurface is very well charac-
terized to the depth of the Lower Jurassic Formation. The
occurrence, thickness and character of older stratigraphic
successions, like the Rhaetian sandstone, investigated here
can only be deduced from deep boreholes outside the
study area and from seismic investigations (Frisch 1993).
The Rhaetian sandstone is the topmost unit of the Keuper
and will therefore be represented in the following by the
Lias depth base (Fig. 2). The area of Allermohe is situated
at the SE margin of the central North German Basin. A
prominent NE–SW striking and SE dipping normal fault
cuts the centre of the Allermohe area (Fig. 1, between the
salt structures). This structure was active during Mesozoic
times (Jaritz 1973), probably due to isostatic compensation
in an extensional tectonic setting, and was reactivated in
Early Tertiary times. From Late Triassic times (Middle
Keuper) until the end of the Mesozoic, extensional normal
faulting caused the uplift of the so-called ‘Hamburg Block’
and the construction of the ‘Quickborn Swell’ (both out-
side the Allermohe map sheet). Salts from the Zechstein
(Upper Permian) and Rotliegend (Lower Permian) accu-
mulated above the faults. The mobilization of the Rotlieg-
end salt raised the overlying Zechstein in some areas and
even partly pierced this formation. This led, most probably,
to the intrusion of Early Permian salts into the diapirs of
Meckelfeld and Reitbrook. The base of the Zechstein is
located at an average depth of 4700–4900 m below mean
sea level (b.s.l.). However, due to halokinesis (deformation
of halite by flowage) the Zechstein base was steeply
inclined and even uplifted up to 4300 m b.s.l. in some
areas. Salt migration resulted in a lowering of the Zech-
stein base to depths of some 5700 m b.s.l. north of the
Meckelfeld salt dome (Frisch 1993). In the SW quadrant
of the Allermohe map sheet, the Meckelfeld salt dome
evolved in the Jurassic, during Dogger times, and at the
eastern margin the Reitbrook salt dome was emplaced a lit-
tle bit earlier, in the Jurassic during Lias times. The upper
surface of the Meckelfeld salt dome is oval and slightly
NE–SW striking with an area of approximately 19 km2
(Fig. 1). Its maximum extent is 7 km · 4 km and it is
hosted within the surrounding Upper Cretaceous forma-
tions. The actual vertical extent of the Meckelfeld diapir is
approximately 3000 m, and it is situated on top of the
major Permian saliniferous residuals (Zechstein, Rotlieg-
end; Frisch 1993). The western upper surface of the Reit-
brook salt dome extends to the eastern margin of the
Allermohe map sheet. It is also ovoid in shape and elon-
gates in the NW–SE direction (Fig. 1). The Reitbrook dia-
pir measures 3–4 km in diameter at its maximum extent.
The salt dome surface has been uplifted to a level of
850 m b.s.l. The overlying Cretaceous and Cenozoic layers
are not pierced by the Reitbrook diapir.
GEOLOGICAL MODEL
Allermohe 3D structure
The 3D model of Allermohe has been obtained by digit-
izing and attributing georeferenced lithological and struc-
tural contour lines of major stratigraphic units from the
‘Tectonic Atlas of Northwest Germany’ (Baldschuhn et al.
2001). To construct surfaces from the data, triangulated
irregular networks (TIN) were computed from the georef-
erenced lithological data and converted to grids with pixel
sizes of 250 m · 250 m and 50 m in depth. Additional
structural features, such as the traces of faults and fold
axes, were incorporated as breaklines for the TIN construc-
tions. The final 3D GIS model measures 11 km · 11 km
and has a depth of 6000 m. The size of the modelling area
was chosen based on analogy with a study by Williams &
Ranganathan (1994) of a setting similar to the North Ger-
man basin in which salt structures are located 10–30 km
apart from each other. The potential Rhaetian reservoir
sandstone is located at the top of the Keuper horizon
(Fig. 2).
Because the structural setting of the Allermohe area is
affected by the intrusion of the two salt domes, Meckelfeld
and Reitbrook, the topography of the Keuper layer is
highly influenced by halokinetic processes. In general, as
seen from Fig. 2, topological relief of the formations
increases with increasing depth. In the SW quadrant of the
area, the Meckelfeld salt dome occurs almost completely
within the study area (Fig. 1). The base of the Keuper lies,
Topography
Tertiary
Upper CretaceousLower CretaceousDoggerLiasKeuperUpper BuntsandsteiLower BuntsandsteiZechstein
Meckelfeld diapir
0
1
2
3
4
5
km b.s.l.
Fig. 2. Structural configuration of Allermohe region measuring 11 km ·11 km with a depth of 6000 m (no vertical exaggeration) and obtained by
digitizing georeferenced structural contour lines of major stratigraphic units
from the ‘Tectonic Atlas of Northwest Germany’ (Baldschuhn et al. 2001).
Compare with Table 1 for petrography.
4D hydrothermal reactive transport model of Allermohe 303
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
depending on its location, between 1800 m and 4500 m
b.s.l.
Cross-sections cut out of the 3D model
From the GIS-based structural grid data (Fig. 2), cross-sec-
tions of any desired orientation (Fig. 1) through the 3D
model can be derived using the program SECTION (Gun-
ther 2003a) to illustrate the complex architecture around
the Allermohe well. Cross-section 1 from west to east,
ending in the Reitbrook salt dome, is displayed in Fig. 3.
The main stratigraphic units (ages and petrography given
in Table 1) are the Cenozoic, Upper and Lower Creta-
ceous, Dogger, Lias, Keuper, Upper and Lower Buntsand-
stein and the Zechstein layer. The diapir, constituted from
Zechstein salt, pierces the overlaying formations from the
Buntsandstein to the Dogger, whereas stratigraphic layers
from the Lower Cretaceous upward are domed up. The
pre-Cretaceous layers descend smoothly away from the
Reitbrook diapir and start to ascend slightly again at a dis-
tance of approximately 6 km to the so-called Hamburg
block, which lies outside the Allermohe map sheet.
The WNW–ESE cross-section 2 (Fig. 4) crosses the
Allermohe well. The stratigraphy is similar to that of cross-
section 1, with the exception that the pre-Cretaceous layers
do not ascend towards the Hamburg block but remain
more or less at the same level. Cross-section 3 (Fig. 5) is
oriented SW to NE and runs through both salt domes.
The pre-Cenozoic layers descend away from the diapirs
Cenozoic (Pleistocene + Tertiary)
Upper CretaceousReitbrook
Zechstein
Dogger
LiasKeuper
Buntsandstein
5 km
W E
Buntsandstein
5 km5 km
W
Fig. 3. Cross-section 1 of the 3D model (compare with Fig. 1 for location;
no vertical exaggeration). The Rhaetian sandstone is located at the top of
the Keuper horizon.
[Correction made 27 June 2007: high resolution figure inserted]
Table 1 Stratigraphic column (TK 2526, sheet Allermohe, Ehlers 1993).
Stratigraphy Petrography (high to low probability) Thickness ca. (m) Time ca. (Myr)
Pleistocene Sand, silt, clay 0–250 0.01–1.7
Tertiary Sand, silt, clay, limestone, shale, sandstone 585–1200 1.7–66
Upper Cretaceous Marlstone, limestone, chalk 290–1000 66–98
Lower Cretaceous Shale, marlstone, sandstone 50–220 98–140
Dogger Shale, marlstone, sandstone 0–900 160–185
Lias Shale 0–1000 185–210
Keuper Shale, marlstone, sandstone, salt, anhydrite, gypsum 250–1000 210–230
Upper Buntsandstein Shale, marlstone, sandstone, salt, dolomite, anhydrite 500–650 245–247
Lower Buntsandstein Sandstone, shale 500–700 247–250
Zechstein Salt, anhydrite, limestone 100–3800 250–270
Rotliegend Shale, sandstone, salt, volcanics Not known 270–290
The Rhaetian sandstone is located at the top of the Keuper horizon.
Cenozoic (Pleistocene + Tertiary)
Upper Cretaceous Reitbrook
Zechstein
DoggerLias
Keuper
Buntsandstein
5 km
WNW ESEAllermöhe
5 km
Fig. 4. Cross-section 2 of the 3D model (compare with Fig. 1 for location;
no vertical exaggeration).
[Correction made 27 June 2007: high resolution figure inserted]
Cenozoic (Pleistocene + Tertiary)
Upper Cretaceous
Reitbrook
Zechstein
Dogger
Lias
Keuper
Buntsandstein
Meckelfeld
5 km
SW NE
Buntsandstein
5 km5 km
Fig. 5. Cross-section 3 of the 3D model (compare with Fig. 1 for location;
no vertical exaggeration).
[Correction made 27 June 2007: high resolution figure inserted]
304 M. KUHN & A. GUNTHER
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
and reach a minimum between them. The formations are
more steeply inclined into the Meckelfeld salt dome than
the Reitbrook salt dome. The deeper layers of the Bunt-
sandstein abut the Reitbrook diapir almost horizontally.
The distance between the diapirs at depth is around 5 km.
Cross-section 4 (Fig. 6) runs NW from the Reitbrook dia-
pir. Characteristic features here are the border between the
Lias and the Keuper, which is nearly horizontal, and the
Buntsandstein layers, which do not show large relief along
this section. The last cross-section shown here runs S–N
(Fig. 7) through the Allermohe well. This cross-section
cuts neither the Meckelfeld diapir nor the Reitbrook salt
dome. The Keuper layer descends slightly towards the cen-
tre of the cross-section and increases in thickness at its
southern and northern borders.
Geological restoration sequence
Previous studies indicate the importance of the structural
geometry on anhydrite transport mechanisms (Kuhn 2004)
and led to investigation of this specific, historic geological
restoration sequence (palinspastic reconstruction). This has
been done to assess stratabound thermal-free convection as
a possible fluid flow driving process in the Rhaetian sand-
stone aquifer. Free convection provides a means of trans-
port for the precipitation of anhydrite but has to be
studied in the context of the evolving structural and litho-
logical geometry resulting from salt tectonics. The basis for
the 3D restoration sequence through time is the structural
model of the study area (Fig. 2). The recent 3D structure
of the Allermohe location is evolved backwards to Keuper
times based on the available geological data. The work has
been done by applying the program RESTORE which
implements a structural modelling algorithm to analyse the
vertical kinematic history from geological cross-section data
(Gunther 2003b). The principle here is the step-by-step
(sequential) restoration of the geological horizons to pre-
deformation and/or presedimentary conditions. For each
restoration sequence all geological horizons were moved
upwards according to vertical shear vectors that were
derived from flattening (straightening) the uppermost hori-
zon of the particular sequence to a fixed elevation datum
(in this case 0 m b.s.l.). All lower stratigraphic horizons to
be restored are moved upwards accordingly. Palaeostruc-
tural models can be derived for a specific geological hori-
zon by restoring it incrementally, by flattening all higher
stratigraphic horizons successively (see Fig. 8 for restor-
ation schema). In this simple restoration approach, both
compaction and isostatic compensation processes have
been neglected. The restoration sequence has been applied
on the Lias depth base because this is equivalent to the
Rhaetian layer at the top of the Keuper. Fig. 9 displays the
shape of the Lias base for different geological times, with
the Meckelfeld salt dome in the foreground and the Reit-
brook diapir in the background. The 4D historic restor-
ation sequence (Fig. 9) is used to examine whether
changing topography of the Rheatian aquifer caused free
Cenozoic (Pleistocene + Tertiary)
Upper CretaceousReitbrook
Zechstein
Lias
Keuper
Buntsandstein
5 km
NW SE
Zechstein
Buntsandstein
5 km5 km
Fig. 6. Cross-section 4 of the 3D model (compare with Fig. 1 for location;
no vertical exaggeration).
[Correction made 27 June 2007: high resolution figure inserted]
Cenozoic (Pleistocene + Tertiary)
Upper Cretaceous
Zechstein
Dogger
Lias
Keuper
Buntsandstein
5 km
S NAllermöhe
ZechsteinBuntsandstein
5 km5 km
N
Fig. 7. Cross-section 5 of the 3D model (compare with Fig. 1 for location;
no vertical exaggeration).
[Correction made 27 June 2007: high resolution figure inserted]
Original bedsRestored beds
Target bed Template bed Shear vectors
Fig. 8. Restoration schema.
[Correction made 27 June 2007: high resolution figure inserted]
4D hydrothermal reactive transport model of Allermohe 305
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
convection-induced flow fields to vary significantly over
geological time, and to determine when and where anhyd-
rite precipitation was most likely in the vicinity of the
Allermohe well.
Numerical model numerical code and process coupling
The Simulator for HEat and MAss Transport (SHEMAT,
Bartels et al. 2003) has been chosen to carry out the
numerical investigations, because with its graphical user
interface ‘Processing SHEMAT’ (Kuhn & Chiang 2003) it
is an easy-to-use, general purpose reactive transport code
for a wide variety of thermal and hydrogeological problems
in two and three dimensions. SHEMAT solves coupled
problems involving fluid flow, heat transfer, species trans-
port and chemical water–rock interaction. It is a finite dif-
ference code that solves the flow and transport equations
on a Cartesian grid. The ‘IAPWS Industrial Formulation’
(Wagner et al. 2000) is the equation of state used for
water. In SHEMAT, the different flow, transport and reac-
tion processes can be selectively coupled. Flow and heat
transport are coupled in that the fluid parameters density,
viscosity, compressibility, thermal conductivity and thermal
capacity are functions of temperature and pressure. Flow
and salt transport are coupled via fluid density implemen-
ted by a linear approximation. Fluid density is of particular
interest and its accurate representation generally vital for
modelling fluid flow in the vicinity of salt structures. Both
thermal effects and varying salinities may induce buoyancy-
driven free convection. SHEMAT’s chemical speciation
module (Kuhn 2003) is a modification of the geochemical
modelling code PHRQPITZ (Plummer et al. 1988). It
permits calculation of geochemical reactions in brines and
other highly concentrated electrolyte solutions using the
Pitzer virial-coefficient approach for ion activity correc-
tions. Reaction-modelling capabilities include calculation of
aqueous speciation and mineral-saturation as well as disso-
lution and precipitation of mineral phases. For a detailed
description of equations incorporated in the program and
code verification the interested reader is referred to the
book ‘Numerical Simulation of Reactive Flow in Hot
Aquifers’ edited by Clauser (2003).
Numerical model set-up
A detailed conceptual model is a prerequisite for numerical
modelling. A conceptual model is qualitative but consistent
with all known geological and hydrological data. A numer-
ical model based on the conceptual model can be used to
test the conceptual model’s quantitative viability. The
Allermohe region is characterized by massive shales, with
up to a 1000-m thickness, above and below the Rhaetian
aquifer. Detailed information about water composition and
rock properties are scarce for the required depth range.
Furthermore, there is ongoing debate in the literature
about cross-formational fluid conduits within argillaceous
settings (Williams & Ranganathan 1994; Sharp et al.
2001). Therefore, we have chosen to run a sophisticated
structural and numerical model based on a simple concep-
tual model (Fig. 10). The focus is solely on the Rhaetian
aquifer itself and the potential of stratabound Rayleigh
convection as a fluid flow driving process that could have
led to the observed anhydrite cementation. The Rhaetian
layer has been extracted from the 3D structure and
assigned a uniform thickness of 250 m. The 3D models
were then overlain and underlain with distinct geological
units representing massive shales known to be above and
below the Rhaetian sandstone (Fig. 10). The resulting
depth range of the numerical model is from 1750 m to
4750 m b.s.l. so the salt domes do not impinge on the
model’s top boundary. Simulations are transient with
respect to fluid flow, heat transfer, species transport and
B: Tertiary structure D: Late Cretaceous structure
C: Early Cretaceous structure E: Middle Jurassic structure
A: Recent structure
570 to 200940 to 5701310 to 9401680 to 13102050 to 1680
2420 to 20502790 to 24203160 to 27903530 to 31603900 to 3530
Meters b.s.l.
Fig. 9. Restoration sequence of the Lias depth base representing the Rhae-
tian top; the foreground displays the Meckelfeld salt dome and the Reit-
brook diapir is situated in the background. The shape of the Lias depth
base is shown for recent times (A), Tertiary (B), Early Cretaceous (C), Late
Cretaceous (D) and Middle Jurassic times (E).
Meckelfelddiapir
Reitbrockdiapir
Shale: k = 10-16 m2 φ = 0.005
Shale
Rhaetian sandstone: k = 4.0x10-13 m2, φ = 0.07
Constant temperature: 60°C
Heat flux: 0.06 W m-2
Depth1750 m
Depth4750 m
3000 mThickness
250 m
Fig. 10. Conceptual model of the Rhaetian layer, embedded into massive
shale layers, extracted from the 3D geological model (Fig. 2).
306 M. KUHN & A. GUNTHER
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
chemical reactions and were conducted for a time period
of 50,000 years for each of the 3D models. The reactive
transport was not coupled in time to the structural evolu-
tion of the model region, but discrete structural configura-
tions at discrete times were modelled. The geologic history
(generic time dimension) from Early Cretaceous times on
was studied in five 3D reactive transport models (Fig. 9A–
E) to investigate varying palaeostructural constraints in the
Rhaetian sandstone. The individual geological 3D struc-
tures of the entire restoration sequence have been trans-
ferred into reactive transport models by discretizing the
modelled areas into cells measuring 250 m · 250 m hori-
zontally with 50-m heights. This means the Rhaetian sand-
stone is discretized by five cells in the vertical direction.
The resulting five models consist of 96 000, 67 200,
59 200, 59 200 and 52 800 cells for the recent structure,
Tertiary, Late Cretaceous, Early Cretaceous and Dogger
times respectively. No-flow, non-reactive simulation runs
were conducted using the model of the recent structure to
determine the purely conductive temperature profile at the
Allermohe well. The numerical models were constructed to
fit the conceptual model (Fig. 10) and major rock types
deduced from the explanations to the geological map of
Hamburg (Ehlers 1993, Table 1). Hence, rock properties
were applied, as listed in Table 2, for rock thermal capacity
(qCP(r)), rock thermal conductivity (kr), porosity (U) and
permeability (k). Rock properties of the Rhaetian sandstone
were obtained from mineralogical investigations of the ori-
ginal Allermohe core material. However, no measurements
of the rock thermal conductivity were available. Therefore,
we applied values of 1.3, 2.5 and 4.5 W m)1 K)1 for the
recent model structure to cover an appropriate range for
sandstones. The models representing the geologic past
(Fig. 9B–E) were performed only with a rock thermal con-
ductivity of 1.3 W m)1 K)1. The initial water composition
was chosen in accordance with formation water analysis
(Table 3). Numerical simulations were performed with a
constant basal heat flow of 0.06 W m)2, corresponding to
published data within the Atlas of Geothermal Resources
of Europe (Hurter & Haenel 2002). At the upper bound-
ary, a constant temperature (e.g. 60�C for the recent struc-
ture) varied according to the burial depth of the particular
model (e.g. 1750 m for the recent structure) and the geo-
thermal gradient. The lateral boundaries of the model are
closed to heat transfer (perfectly insulated). All six bound-
aries are impermeable, defining a closed box with no
sources or sinks for the pore fluid. The initial hydraulic
heads were defined on the basis of burial depths ranging
from 4500 m for the recent structure to 1650 m for the
Dogger structure. We exclude regional flow based on the
findings of Muller & Papendieck (1975), who inferred
stagnant water conditions in the formations of the Rhaet
from chemical and isotopic analyses of the formation
waters.
We assume that calcium and sulphate and sodium chlor-
ide are available as anhydrite and halite, respectively, from
the salt structures only. The chemical calculations are based
on the ‘equilibrium’ assumption that reaction rate is very
fast compared with other processes involved. This neglects
reaction kinetics, consistent with the fact that the satura-
tion length of anhydrite is much less than the dimensions
of the model cells (Bartels et al. 2002). The Rhaetian sand-
stone is initially assumed to be totally free of anhydrite.
The aim is to determine anhydrite precipitation patterns
for the entire area of the Allermohe map sheet and to
investigate whether precipitation of anhydrite may occur at
the Allermohe well due to anhydrite dissolution from the
diapirs and transport of calcium and sulphate through the
regional structures.
RESULTS OF REACTIVE TRANSPORTMODELLING
Recent structure
Simulated temperature can be compared with down hole
temperature survey conducted before the pumping test in
1998 to assess whether the simulated thermal field is rea-
sonable; few other deep data are available for comparison
with the numerical results. Both purely conductive and
coupled flow and heat transfer models show reasonable
agreement (Fig. 11). Free thermal convection results from
an unstable distribution of fluid density because of tem-
perature or salinity differences. When a porous medium is
heated from below, cool, dense fluid is at the top and hot,
less dense fluid at the bottom of the system. This situation
is gravitationally unstable, because cool fluids tend to sink
and hot fluids tend to rise, eventually leading to free ther-
mal convection. This instability is intensified by the flow
towards the diapirs, where the water dissolves salt and
becomes more dense, then sinks between the diapirs. For
the recent Allermohe structure (Fig. 9A) free thermal
Table 2 Rock properties applied for numerical simulations with data from
Grober et al. (1963), Mercer et al. (1982) and Neuzil (1994).
Rock type
q CP(r)
(MJ m)3 K)1)
kr
(W m)1 K)1)
U
(–)
k
(m2)
Shale 2.04 1.28 0.005 1.0E)16
Salt 1.95 6.1 0.0001 0.0
Rhaetian sandstone 1.6 1.3/2.5/4.5 0.07 0.4E)12
Table 3 Composition of the Allermohe formation water (Lenz et al. 1997)
with total dissolved solids of 218 g l)1, density 1.146 g l)1 and pH 5.4.
Ion
(mg l)1)
K+ Na+ Ca2+ Mg2+ Cl) SO2�4 HCO�3
1250 75 000 6690 1300 132 200 465 240
4D hydrothermal reactive transport model of Allermohe 307
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Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
convection occurs and the evolved flow field turns clock-
wise. Starting from the western border of the Reitbrook
salt dome (Fig. 12) the main flow is directed south, down
the relief of the Rhaetian layer. Approximately 2000 m
south of Reitbrook, flow turns west towards the Meckel-
feld diapir and, ca. 1500 m north of the Meckelfeld diapir,
the main flow direction is guided north down to the deep-
est point of the formation (Fig. 12, see also Fig. 1). Com-
ing out of the trough, the brine flows upwards towards the
Allermohe well and backwards to the Reitbrook diapir.
Classic Rayleigh convection theory was developed in the
context of an infinite, permeable horizontal layer bounded
at the top and bottom by isothermal, impermeable forma-
tions (Lapwood 1948). The dimensionless Rayleigh num-
ber (Ra), indicating the tendency of a system towards free
convection, is based on the ratio of buoyant forces that
drive fluid flow to the viscous forces inhibiting fluid move-
ment. The present model scenario differs from the classic
Rayleigh scenario in that here the lower boundary condi-
tion is constant heat flux instead of constant temperature,
and the convection occurs on an inclined rather than on a
vertical plane. No analytical solution has yet been deduced
for a system as heterogeneous and complex as that of
Allermohe. Therefore, any calculation of Ra, after either,
e.g. Ingebritsen & Sanford (1998) for the purely thermally
driven case of free convection, or Nield (1968) for a sali-
nity-driven case, is not strictly valid. However, determina-
tion of Ra, here following Ingebritsen & Sanford (1998),
because no salinity gradients were initially implemented in
the numerical model, results in values between 188 and
652 for rock thermal conductivities of the Rhaetian sand-
stone from 4.5 to 1.3 W m)1 K)1 respectively. All values
are well above the critical Ra of 4p2 and fluid flow convec-
tion patterns are identical for all three applied rock thermal
conductivities. Although the theoretical Ra can only very
roughly indicates the tendency of the Allermohe system
towards free convection, the high Ra numbers calculated
suggest that free convection is likely to have occurred,
which is consistent with the numerical results. Wood &
Hewett (1982) have also studied free thermal convection
in inclined layers. They realized that fluid motion takes the
form of closed loops, which are located across the vertical
extent of permeable layers, with fluid motion up dip along
the warmer, lower boundary and down dip along the
cooler, upper boundary. This kind of free thermal convec-
tion is not possible within our model because thickness of
the Rhaetian sandstone is insufficient. Our results show
that stratabound convection in inclined layers is possible
with down-flow regions laterally separated from the
up-flow regions. The clockwise direction of the thermal
convection flow field results from the thermal effects of the
salt domes, which owe to their high thermal conductivity
relative to the surrounding rock (Table 2). Around shallow
parts of a salt dome, temperature iso-surfaces bulge up, so
that the surrounding rock is heated by the salt structure.
Around deeper parts, iso-surfaces bulge down and the salt
dome cools surrounding rock masses. The Rhaetian sand-
stone is located around the deeper parts of the Reitbrook
and Meckelfeld diapirs (Fig. 2). Thus, the NW quadrant
(Fig. 1), due to its distance from the salt structures, is the
hottest area in the Rhaetian sandstone. Water migrates up-
dip (cross-section 2, Fig. 4) towards the Allermohe well,
cools in the vicinity of the Reitbrook diapir, and sinks
along cross-section 3 (Fig. 5) into deeper parts of the
Rhaetian sandstone between the salt diapirs. We can con-
clude that the geometry is the first-order control on ther-
mal patterns and as a consequence the clockwise turning
direction of the flow field. The temperature depth profile
of the coupled numerical simulation at the position of the
Allermohe well shows an excellent fit for the entire inter-
section between field observations and numerical computa-
Fig. 11. Temperature survey from 1998 compared with results of numer-
ical simulations based on the Rhaetian layer extracted from the 3D struc-
ture of the Allermohe site (Figs 2 and 10).
Fig. 12. Plan view of the modelled area (Allermohe map sheet) for the
recent structure (Fig. 9A) showing the Allermohe well (black square) and
the Meckelfeld (SW) and Reitbrook (E) diapirs. The arrows display the Dar-
cian flow field from the 3D simulation. Black arrows represent areas where
anhydrite precipitation in the Rhaetian sandstone exceeds 10 mol m)3 after
a simulated time period of 50,000 years.
[Correction made 27 June 2007: high resolution figure inserted]
308 M. KUHN & A. GUNTHER
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
tions from 1750 m to 3250 m depth, including the depth
range of the Rhaetian sandstone from 3000 m to 3250 m
(Fig. 11). Although free Rayleigh convection is observed,
the temperature profile still looks conduction dominated,
with a slightly increased gradient compared with the purely
conductive reference model. The black arrows in Fig. 12
indicate areas anhydrite precipitation amounts exceeding
10 mol m)3 due to transport of solutes from the salt struc-
tures and subsequent precipitation of anhydrite. This
threshold value was chosen to delineate areas of precipita-
tion. To entirely occlude the initial porosity of the Rhae-
tian sandstone, about 1500 mol m)3 of anhydrite is
required (determined from rock samples). Anhydrite is a
retrograde dissolving mineral that increases in solubility
with decreasing temperature. As shown by Kuhn et al.
(2002), anhydrite solubility is far more sensitive to tem-
perature than it is to salinity for the investigated ranges of
60–180�C, and 3.0–5.5 mol l)1 NaCl respectively. For any
given temperature, anhydrite solubility is almost constant
over this salinity range. Hence, temperature governs an-
hydrite precipitation and dissolution in our numerical si-
mulations. Anhydrite in thermodynamic equilibrium with
respect to the brine at the salt domes is going to precipi-
tate when flow is downwards, following the shape of the
Rhaetian aquifers, and conversely will dissolve where flow
is ascending. In the simulation, significant amounts of
anhydrite are present only in the southern parts of the
investigated area, not around the Allermohe well. Flow
towards the location of the Allermohe well is directed
upwards along the Rhaetian sandstone, leading to
decreased temperatures and lowering the probability of
precipitation. It is unlikely that excess of calcium and sul-
phate leached from the salt dome would reach the location
of the Allermohe well unless free thermal convection
occurred in the anti-clockwise direction. Temporal develop-
ment of the sodium chloride and calcium concentrations at
the Allermohe site, based on the recent structure, is shown
in Fig. 13. The system develops from initial conditions to
equilibrium within approximately 20,000 years with flow
velocities around 1 m per year (Fig. 12). Whereas tempera-
ture approaches the observed value of 125�C and calcium
concentration remains almost constant, the sodium chlo-
ride concentration increases from the observed amount of
around 3000 mmol l)1 to values above 5000 mmol l)1.
These results can be interpreted in at least two different
ways: (1) a horizontal convection cell does exist, consistent
with the agreement of measured and simulated tempera-
ture profile and Ca concentration. However, the sodium
chloride contents of the formation water may not be gov-
erned by thermodynamic equilibrium in combination with
a permeable dome-aquifer contact zone as assumed in the
simulations. If this contact zone were less permeable, due
to salt sealing the pore space, the transport of sodium and
chloride from the dome into the aquifer could be diffusion
controlled. (2) A stratabound Rayleigh convection cell
does not exist, and the processes of halite dissolution and
precipitation are adequately reproduced in the model. In
this case the fluid flow conditions are not driven by strat-
abound convection, but rather by cross-formational flow.
Cross-formational flow would be facilitated by over-pres-
sured deeper formations and faults and fractures that allow
fluid flow into overlying units.
Restoration sequence (geological history)
As stated before, the evolving flow field within a geologi-
cal system strongly depends on the geometry. The palaeo-
structural geological systems (Fig. 9) were investigated in
the same manner as the recent 3D model (see above). In
none of the cases did anhydrite precipitation occur within
the vicinity of the Allermohe well. The oldest investigated
geological structure is the one representing Dogger times
(e.g. the Dogger base lying flat at 0 m b.s.l.) with the
Lias layer being the uppermost stratigraphic unit. Diapi-
rism had already led to the formation of the salt domes
of Meckelfeld and Reitbrook. The Rhaetian formation dis-
plays only a weak relief in which little free thermal con-
vection evolves. This is in accordance with a comparably
low Rayleigh number for the system of 72 (for a rock
thermal conductivity of 1.3 W m)1 K)1). No significant
precipitation of anhydrite is observed and the results are
not shown here. The next generic structure is the one
representing Early Cretaceous times with the Dogger layer
being the uppermost stratigraphic unit (Fig. 14). The
Rhaetian layer has stronger relief compared with Dogger
times, resulting in a Rayleigh number of 176 (for a rock
thermal conductivity of 1.3 W m)1 K)1). Fluid flow can
be observed throughout the entire area and in the vicinity
of the Allermohe well. However, subsequent anhydrite
precipitation (black arrows) is sparse. The model shows
no active flow field that would be able to transport suffi-
cient solutes from the salt domes to the Allermohe well.
110
120
130
140
150
160
170
0 10 000 20 000 30 000 40 000 50 000
Time (years)
Ca
(mm
ol l
–1),
Tem
per
atu
re (
°C)
2000
2500
3000
3500
4000
4500
5000
5500
6000
NaC
l (m
mo
l l–1
)
Calcium
Temperature
Sodium chloride
Fig. 13. Variation of temperature, sodium chloride and calcium content at
the Allermohe well from initial conditions to a simulated time period of
50,000 years within the recent 3D structure (Fig. 9A).
4D hydrothermal reactive transport model of Allermohe 309
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Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
Fig. 15 exhibits the situation in Late Cretaceous times,
when the Lower Cretaceous stratigraphic unit was the
uppermost layer of the 3D structure. Compared with
Early Cretaceous times (Fig. 14) the flow field has chan-
ged significantly, in such that the main reactive area is
situated in the NW of the map sheet. Fluid flow is
enhanced due to a larger Rayleigh number (here 225 for
1.3 W m)1 K)1) that owes to increasing topography of
the Rhaetian sandstone. The Allermohe well is situated in
the centre of a small stratabound convection cell in con-
tact with the Reitbrook salt structure. However, anhydrite
precipitation around the Allermohe well is not indicated.
The flow field consists of a number of smaller convection
cells compared with the large cell existing within the
recent structure (Fig. 12). Fig. 16 displays the flow field
resulting from the geologic structure at the Allermohe site
during Tertiary times when the Upper Cretaceous layer
was the topmost stratigraphic unit. The pattern of flow
has not changed much from the previous historic stage
(Fig. 15), but the intensity of flow has increased substan-
tially. This is due to the fact that both formation tem-
perature and formation topography increase with burial
depth and as a consequence viscosity decreases and the
thermal gradient increases respectively. Both effects result
in an increased Rayleigh number, which is now 389 (with
rock thermal conductivity 1.3 W m)1 K)1), enhancing the
probability of free thermal convection and intensifying
fluid flow velocities. Significant amounts of anhydrite pre-
cipitate in the southern part of the Allermohe map sheet,
north of the Meckelfeld diapir and between both salt
structures. A clockwise convection cell again occurs in the
vicinity of the Allermohe well. The NW quadrant exhibits
high flow rates but no precipitation of anhydrite.
CONCLUSIONS
The installation of a GHS at the Allermohe location failed
because the target aquifer, the Rhaetian sandstone, was
unexpectedly and extensively mineralized by anhydrite,
reducing porosity and permeability. Although the tempera-
ture and thickness of the aquifer are well suited for geo-
thermal energy production, the extractable amount of
water is too low for an economical use of the resource.
Reactive transport simulations have been conducted to
help understand the observed cementation. Free strat-
abound Rayleigh convection has been shown to be
Fig. 15. Plan view of the modelled area (Allermohe map sheet) during Late
Cretaceous times (Lower Cretaceous ¼ top of stratigraphy).
[Correction made 27 June 2007: high resolution figure inserted]
Fig. 14. Plan view of the modelled area (Allermohe map sheet) during
Early Cretaceous times (dogger ¼ top of stratigraphy).
[Correction made 27 June 2007: high resolution figure inserted]
Fig. 16. Plan view of the modelled area (Allermohe map sheet) during Ter-
tiary times (Upper Cretaceous ¼ top of stratigraphy).
[Correction made 27 June 2007: high resolution figure inserted]
310 M. KUHN & A. GUNTHER
� 2007 The Authors
Journal compilation � 2007 Blackwell Publishing Ltd, Geofluids, 7, 301–312
first-order dependent on the geometry of the geological
structure. The temporal development of sodium chloride
concentration (Fig. 13) at the Allermohe well suggests that
either the simulation of NaCl dissolution at the salt dome–
sandstone contact is not accurate enough, or that fluid-
flow drivers other than stratabound Rayleigh convection
need to be taken into account, including processes like
cross-formational flow. The simulations of the entire 3D
historical restoration sequence show the area around the
Allermohe well to be free of anhydrite precipitation during
the geologic past (Figs 12, 14–16). Instead, precipitation
occurs predominantly in southern parts of the investigated
area. The free thermal convection patterns become more
organized and the intensity of the observed fluid flow
increases substantially with burial depth of the formation.
We find that the hypothesis of Lenz et al. (1997) regard-
ing stratabound Rayleigh convection as the process con-
trolling anhydrite precipitation cannot be proven. Their
assumption that the observed anhydrite cementation at the
location of the Allermohe well may be due to solutes lea-
ched from the salt structures, transported through the sys-
tem, and subsequently precipitated, requires a transport
mechanism different from the one investigated here.
Future work will focus on coupling reactive transport
simulations to more sophisticated palaeostructural models,
such that the evolving material parameters of the aquifer
through time (i.e. permeability, porosity and conductivity)
will be incorporated into the restoration process. More-
over, the influence of both local and regional isostatic
effects on the palaeostructural environments will be mod-
elled. This seems particularly important with respect to
halokinetic influences on the structural geometry of the
Allermohe test site. Next, the incorporation of the faults
are crucial to improve the quality of the structural models,
in such that movement along these at particular geological
time intervals will clearly modify the palaeostructural
geometries and also might initiate or facilitate cross-
formational flow to some extent. Our current structural
modelling approach represents a first approach to loose
coupling of palaeostructural and reactive transport models
to study observed mineralization patterns. For further
simulations it is planned to build a 3D numerical model
from the entire 3D geological GIS model presented here
and to investigate cross-formational flow due to thermo-
haline convection and other probable fluid flow drivers.
The reaction boundaries will be refined to evaluate whether
thermodynamic equilibrium is an accurate description of
the chemical processes or if a kinetic approach needs to be
considered.
ACKNOWLEDGEMENTS
Research work reported here was supported by the German
Federal Ministry for Economic Affairs (BMWi) under grant
032 70 95. Special thanks are given to Martin Appold,
Steve Ingebritsen and Ward Sanford for their highly con-
structive reviews.
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