Advances in Water Resources 86 (2015) 32–45
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Advances in Water Resources
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Salinization in a stratiﬁed aquifer induced by heat transfer
from well casings
Jan H. van Lopika,b,∗, Niels Hartoga,b, Willem Jan Zaadnoordijkb,c, D. Gijsbert Cirkelb,
aUtrecht University, Department of Earth Sciences, Budapestlaan 4, 3584 CD Utrecht, The Netherlands
bKWR Watercycle Research Institute, Groningenhaven 7, 3433 PE Nieuwegein, The Netherlands
cDelft University of Technology, Water Resources Section, Faculty of Civil Engineering and Geosciences, Stevinweg 1, 2628 CN Delft, The Netherlands
a r t i c l e i n f o
Received 21 January 2015
Revised 24 September 2015
Accepted 25 September 2015
Available online 9 October 2015
Wellbore heat transmission
Non-linear density equation
a b s t r a c t
The temperature inside wells used for gas, oil and geothermal energy production, as well as steam injection,
is in general signiﬁcantly higher than the groundwater temperature at shallower depths. While heat loss
from these hot wells is known to occur, the extent to which this heat loss may result in density-driven ﬂow
and in mixing of surrounding groundwater has not been assessed so far. However, based on the heat and
solute effects on density of this arrangement, the induced temperature contrasts in the aquifer due to heat
transfer are expected to destabilize the system and result in convection, while existing salt concentration
contrasts in an aquifer would act to stabilize the system. To evaluate the degree of impact that may occur
under ﬁeld conditions, free convection in a 50-m-thick aquifer driven by the heat loss from penetrating hot
wells was simulated using a 2D axisymmetric SEAWAT model. In particular, the salinization potential of fresh
groundwater due to the upward movement of brackish or saline water in a stratiﬁed aquifer is studied. To
account for a large variety of well applications and conﬁgurations, as well as different penetrated aquifer
systems, a wide range of well temperatures, from 40 to 100 °C, together with a range of salt concentration (1–
35 kg/m3) contrasts were considered. This large temperature difference with the native groundwater (15 °C)
required implementation of a non-linear density equation of state in SEAWAT. We show that density-driven
groundwater ﬂow results in a considerable salt mass transport (up to 166,000 kg) to the top of the aquifer in
the vicinity of the well (radial distance up to 91 m) over a period of 30 years. Sensitivity analysis showed that
density-driven groundwater ﬂow and the upward salt transport was particularly enhanced by the increased
heat transport from the well into the aquifer by thermal conduction due to increased well casing temperature,
thermal conductivity of the soil, as well as decreased porosity values. Enhanced groundwater ﬂow and salt
transport was also observed for increased hydraulic conductivity of the aquifer. While advective salt transport
was dominant for lower salt concentration contrasts, under higher salt concentration contrasts transport was
controlled by dispersive mixing at the fresh-salt water interface between the two separate convection cells
in the fresh and salt water layers. The results of this study indicate heat loss from hot well casings can induce
density-driven transport and mixing processes in surrounding groundwater. This process should therefore be
considered when monitoring for long-term groundwater quality changes near wells through which hot ﬂuids
or gases are transported.
© 2015 Elsevier Ltd. All rights reserved.
Oil and gas deposits, as well as exploitable geothermal energy,
are typically found in reservoirs well below the depths of exploitable
fresh groundwater supplies. Therefore, wells for conventional oil
∗Corresponding author at: Utrecht University, Department of Earth Sciences, Envi-
ronmental Hydrogeology Group, Budapestlaan 4, 3584 CD Utrecht, The Netherlands.
Tel: +31 631697963.
E-mail address: firstname.lastname@example.org,email@example.com (J.H. van Lopik).
and gas, shale gas and geothermal energy production fully penetrate
shallow fresh water aquifers. The temperatures of wellbores during
oil production , gas production , geothermal energy produc-
tion  and hot water or steam injection , can be signiﬁcantly
higher (e.g., T>40 °C) than the typical temperatures of the shallow
aquifers in moderate climates (10–20 °C). The temperature difference
causes heat transfer to the surrounding formations and cooling of
the ﬂuid or gas that is ﬂowing inside the well . The resulting
temperature at the wellhead is important for operational drilling
and injection/production aspects, such as determining viscosity and
0309-1708/© 2015 Elsevier Ltd. All rights reserved.
J.H. van Lopik et al. / Advances in Water Resources 86 (2015) 32–45 33
Fig. 1. Thermally induced density-driven ﬂow due to heat transfer from a well to the aquifer and its effect on fresh-salt stratiﬁed groundwater (parameter values belong to the
reference scenario used in this study).
thereby ﬂowing pressure changes in a heavy-oil well, or estimating
steam quality during steam injection. However, to our knowledge,
the thermal effects of wellbore heat losses for the aquifers that
receive the heat have not been addressed.
Many studies have investigated density-driven ﬂow in porous
media under the inﬂuence of temperature contrasts in groundwater
systems (e.g. [4,15]). This can occur both at large scale, like geother-
mal convection in geological basins , or at small scale such as
the upward density-driven ﬂow of injected hot water during high
temperature aquifer thermal energy storage (e.g. [2,27,42,44]). In
addition to temperature, density-driven groundwater ﬂow is affected
by salt concentration contrasts. The effect of salt concentration and
temperature gradients on convective ﬂow patterns in thermo-haline
systems were studied by [4,17,29,36,39]. A few studies have focused
on thermo-haline convection on ﬁeld scale; e.g. the effect of hyper-
saline cooling canals on aquifer salinization  and the transport of
hot, brine water plumes .
Thermal convection under the inﬂuence of a vertical heat source
like a vertical ﬂat plate  or long vertical thin blades  in a porous
medium has been investigated numerically. These geophysical ex-
amples suggest that hot wellbores penetrating cooler aquifers could
thermally induce density-driven groundwater ﬂow.
In many aquifers, fresh groundwater overlies denser, saline water
and salinization by mobilization of the underlying saline water is con-
sidered a major threat to fresh groundwater resources and drinking
water production [5,34,48]. Local thermally induced density-driven
ﬂow in the vicinity of hot well casings could therefore result in mixing
and deterioration of the groundwater quality (see Fig. 1). To explore
this possibility, we simulated transient temperature and salinity de-
pendent density-driven groundwater ﬂow along a hot wellbore. We
used SEAWATv4, and further include a non-linear density equation of
state, to apply to various thermal conditions, salt concentration con-
trasts and aquifer properties.
2. Theory and methodology
2.1. Wellbore heat transmission
Fluid or gas ﬂowing in the wellbore loses heat to its surroundings
by thermal conduction due to the difference between wellbore ﬂuid
and surrounding aquifer temperature during injection or production
operations. The heat transfer from the wellbore is proportional to
the thermal resistance of the well system, including the tubing wall,
annulus, casing wall and cement sheets. Ramey  introduced
an approximate, analytical solution for wellbore heat transmission
to estimate wellhead temperature as a function of wellbore depth
and the operational time. He has developed solutions for ﬂuids and
perfect gasses, assuming steady-state ﬂuid ﬂow in the wellbore and
transient heat conduction into the formation. An overall heat transfer
coeﬃcient was introduced to account for the total thermal resistance
of the well system. Other studies introduced methods to account for
multiple formation layers with different physical properties , for
real gas production , or for two-phase ﬂow in the wellbore .
Wellhead temperature distributions during oil, gas and geothermal
energy production, as well as temperature distributions of steam and
hot water injection applications, show that the difference between
wellbore ﬂuid temperature and surrounding formation at shallow
depths can be signiﬁcant with temperature differences larger than
30 °C[6,11,13,35,50]. However, the effective temperature of the outer
well casing may differ from the wellbore ﬂuid temperature, depend-
ing on the total thermal resistance of the well system. In general,
thermal resistance of steel casings and tubings can be neglected,
while insulating materials like cement sheets and annuli ﬁlled with
liquid or gas have a high thermal resistance. According to Ramey
, heat transfer through the different thermal resistance elements
of the wellbore is considerably faster than heat transfer in the sur-
rounding formation and, therefore, may be assumed as a steady-state
We have used SEAWATv4 [10,24] to model density-driven
groundwater ﬂow induced by heat transfer from a hot well cas-
ing. SEAWATv4 is a coupled version of the simulation programs
for groundwater ﬂow, MODFLOW2000  and for multi-species
mass transport, MT3DMS , together with a variable density and
viscosity package. This enables the simulation of variable-density
groundwater ﬂow combined with heat and multi-species solute
transport. The differential equation for solute transport takes into
34 J.H. van Lopik et al. /Advances in Water Resources 86 (2015) 32–45
account advection, dispersion and molecular diffusion:
where Cis the concentration of the solute (kg/m3), tis the time (d),
qis the speciﬁc discharge, ρbis the bulk density (kg/m3), Kdis the
distribution coeﬃcient (m3/kg), Dmis the molecular diffusion coeﬃ-
cient (m2/d), θis the porosity, α(m) is the dispersivity coeﬃcient, qs
is the source or sink (m/d) and Csis the source or sink concentration
(kg/m3). We have followed Langevin  and employed solute
transport equations to simulate heat transport in the aquifer:
ρcp f ¶δ(θT)
The molecular diffusion coeﬃcient, as input parameter, can be used
to describe conductive heat transport by deﬁning a bulk thermal
where λfand λs(W/m °C) are the thermal conductivity of water and
solid phase, respectively, cpf is the heat capacity of water (J/kg °C)and
ρis the water density (kg/m3). Moreover, thermal equilibrium be-
tween water and the solid phase during heat transport is represented
by a thermal distribution factor, KdT (m3/kg):
where cps (J/kg °C) is the heat capacity of solid phase. Therefore,
thermal retardation can be described in a similar manner as solute
θKdT where ρb=ρs(1−θ)(5)
where ρs(kg/m3) is the solid phase density.
SEAWATv4 uses the Oberbeck–Boussinesq approximation (e.g.
) to assume a constant ﬂuid density in the heat transport equation,
while ﬂuid density is a function of salt concentration and tempera-
ture in the buoyancy term . Assuming a constant ﬂuid density
(ρ) and the heat capacity of the ﬂuid (cpf) simpliﬁes the heat trans-
port equation (Eq. (2)) and enables the use of a constant bulk ther-
mal diffusivity (DT) and thermal distribution factor (KdT). We have
used a ﬂuid density (ρ) of 1000 kg/m3to calculate these parameters.
At high temperature and salt concentration contrasts the Oberbeck–
Boussinesq approximation becomes insuﬃcient [4,21]. In our sim-
ulated scenarios large temperature contrasts between well casing
(80 °C) and background groundwater temperatures are used, as well
as large salt concentration contrasts (0–35 kg/m3). Maximum ﬂuid
density is that of seawater (Cs=35 kg/m3) at a temperature of 15 °C
with a value of 1027 kg/m3. Close to the wellbore, the water is heated
up to 71.5 °C, resulting in a ﬂuid density of 977 kg/m3. Considering
these densities, the likely change in the bulk thermal diffusivity term
(DT) and the thermal distribution factor (KdT) can be calculated with
Eqs. (3) and (4). The relative error for DTand KdT is ±2.5% while using
the ﬂuid density of 1000 kg/m3as a reference. This means that the re-
sulting minimum and maximum DTvalues are 0.124 and 0.129 m2/d,
respectively. For KdT, these values are 1.86Å10−4and 1.96Å10−4m3/kg
and the error in heat transport due to the Oberbeck-Boussinesq ap-
proximation will be negligible .
The Boussinesq approximation in SEAWAT also simpliﬁes the con-
tinuity equation such that the volume of water is not inﬂuenced
by temperature and salinity, but only by head . This means the
source terms nρbT∂T/∂tand nρbC∂C/∂tare neglected with respect to
ρSs∂h/∂t, where bTand bCare the thermal and solute coeﬃcient of
water expansivity, respectively. Our study has ranges of temperature
from 20 to 60 °C, salinity from 0 to 35 kg/m3, and head variation of
0.5 m. Using values of bT=4.3Å10−4°C−1and bC=7.3Å10−4m3/kg,
this means this assumption is not warranted. However, the volume
changes do not have a large inﬂuence on the ﬂow in our study.
The inﬂuences on the volume are strongest near the well, uniformly
over the thickness of the aquifer. The related pressure changes dissi-
pate laterally so that the upward convection along the well hardly is
2.3. Equation of state
Equations of state describe the temperature and salinity depen-
dence of properties of water, such as density, viscosity, heat capacity,
and thermal conductivity. SEAWATv4 allows for equations of state for
ﬂuid density and viscosity. The following viscosity equation  is
used in SEAWAT:
µ(C,T)=2.394 ·10−5·³10 248.37
T+133.15 ´+1.92 ·10−6(C−C0)(6)
where µis the dynamic viscosity (kg/m s), Cis the salt concentration
(kg/m3) and Tis the temperature of the ﬂuid.
The current standard SEAWATv4 computer code allows only for a
linearized form of the density equation of state:
This linear form of the density equation of state is used in many
groundwater ﬂow and heat transport codes, like SUTRA  and
HST3D . However, the density–temperature relationship is in-
deed non-linear (e.g. [26,37,38,41,49]). It can only be linearized with a
δρ/δTerror of less than 5% for temperature ranges in the order of 2 °C
for low water temperatures (∼20 °C) and for temperature ranges in
the order of 10 °C for higher water temperatures (∼60 °C) (see Fig. 2).
For a wide range of temperature and salinity, Sharqawy et al. 
derived an empirical non-linear density relationship based on exper-
imentally derived datasets for both salinity and temperature at 1 atm
pressure from Isdale and Morris  and Millero and Poisson :
ρ(T,S)=(999.9+2.034 ·10−2T−6.162 ·10−3T2
+2.261 ·10−5T3−4.657 ·10−8T4)
1000 −2.001 S
1000 T+1.677 ·10−2S
1000 T3−1.613 ·10−5³S
where Sis the salinity (g/kg) and Tis the temperature (°C). This den-
sity relationship (Fig. 3) is valid for a temperature range of 0–180 °C
and a salinity range of 0–160 g/kg with an accuracy of ±0.1%.
Previous simulation studies on density-driven groundwater ﬂow
have used different density equations of state (Table 1). Thorne et al.
 and Langevin et al.  veriﬁed SEAWATv4 by modeling the
Henry–Hilleke problem with the temperature and salt concentration
ranges shown in Fig. 3. Their linear approximations for the density–
temperature relationship are shown in Fig. 2. Holzbecher  and
Tsang et al.  have used a non-linear density–temperature rela-
tion (Table 1) based on empirical relationships derived by Tilton and
Taylor  and Wooding , respectively.
The conditions for density-driven groundwater ﬂow in our study
span large temperature contrasts between a well casing (up to 100 °C)
and background groundwater temperatures of 15 °C, as well as large
salt concentration contrasts (0–35 kg/m3). First, we have investigated
the effect of using a non-linear density equation in the SEAWATv4
code for the reference scenario (Case 1) and compared these re-
sults with a scenario run with the conventional SEAWATv4 code us-
ing the linear density equation of state (Case 1.1). A linear density–
temperature approximation for the conditions considered in this
J.H. van Lopik et al. / Advances in Water Resources 86 (2015) 32–45 35
Fig. 2. Dependence of density–temperature gradient on temperature based on the density equation of state as listed for each study in Table 1, while considering fresh water
(S=0 g/kg). The gray line shows the linear approximation over the temperature range 15–80 °C at a salinity value of 17.5 g/kg based on Eq. (8). These dρ/dT gradient is used
for our modeling study (Case 1.1).
Fig. 3. Water density [kg/m3] at different temperature and salinity values calculated
with Eq. (8) , where the used salinity and temperature ranges are shown for the
studies listed in Table 1 and the present study.
study was derived from Eq. (8) by linear interpolation of the mini-
mum and maximum density values. For the linear approximation of
the reference scenario (Case 1.1), the temperature range of 15–80 °C
and the average salinity value of the aquifer system (17.5 g/kg) were
used. This results in a dρ/dT gradient of −0.434 (Fig. 2, Case 1.1). The
linear density approximation over this temperature range yields a de-
viation from the non-linear relationship (Eq. (8), with S=17.5 g/kg) at
both low and high ends, respectively with an overestimation and un-
derestimation of the density–temperature gradient by approximately
a factor 2. To determine the effect of deviations caused by the lin-
earization of the density relationship on modeling density-driven
ﬂow, we have also implemented the empirical non-linear equation
(Eq. (8)), developed by Sharqawy et al. , in the SEAWATv4 code.
An iterative algorithm was implemented to calculate the ﬂuid den-
sity from the salt concentration (Cs) and temperature (see Fig. 4). Clo-
sure of the iterative process was set at a relative density difference of
1Å10−3. The source code implementation is given in Appendix A.
2.4. Model setup
We considered a homogeneous conﬁned sandy aquifer with a
horizontal interface between fresh and saline groundwater at 40 m
depth (10 m above the aquifer bottom). The groundwater ﬂow was
simulated axi-symmetrically, following the approach of Langevin
 which has been validated for transport of solutes  and
We assumed a constant effective temperature of the outer well
casing, to simulate the heat loss from the well. Analytical and ﬁeld
Density equation of state in previous variable-density groundwater modeling studies.
Study T-range [°C] Cs-range [kg/m3] Density equation of state Code
Langevin et al.  6.1–73.9 0–35 ρ=1000 +0.78C−0.392(T−14)SEAWAT
Thorne et al.  5–50 0–35.7 ρ=1000 +0.7C−0.375TSEAWAT
Vandenbohede et al.  7.85–48 0 ρ=1000 −0.375(T−10)SEAWAT
Tsang et al.  20-55.4 0 T>25 °C: ρ=996.9[1 −3.17·10−4(T−25)
−2.56 ·10−6(T−25)2]T<25 °C:
ρ=996.9[1 −1.87 ·10−4(T−25)]
Holzbecher  0-40 0 ρ=(1−(T−3.9863)2
T+68.12963 )·1000 FAST_C(2D)
36 J.H. van Lopik et al. /Advances in Water Resources 86 (2015) 32–45
Fig. 4. Flowchart for the non-linear density calculation in the SEAWAT code.
studies have shown that in many cases the bore-face temperature at
a given depth can be considered constant [22,35]. The heat transport
through the well casing elements can be considered rapid compared
to heat transport into the surrounding aquifer and can be considered
steady-state . In addition, we assumed that the effective well cas-
ing temperature (Tc) is constant over the entire aquifer thickness of
only 50 m. Using Ramey’s solution , this is a reasonable assump-
tion for this limited depth range.
In the axi-symmetric transient model, a radius of 500 m and
aquifer thickness of 50 m was used. The grid resolution in the model
domain is 1r=0.25 m by 1z=0.5 m for [0.5 <r<23], 1r=0.5 m
by 1z=0.5 m for [23 <r<180] and 1r=1 m by 1z=0.5 m for
[180 <r<500]. The well system is 0.499 m thick, where the ﬁrst
column, representing the wellbore, is deﬁned as a no-ﬂow boundary.
The second column is only 0.001 m thick and represents the outer
well casing with a constant effective well casing temperature (Tc). The
initial aquifer temperature is 15 °C and the initial salt concentration
is 0 kg/m3for [0 <z<40] and Cs[40 <z<50] (see Table 2). The
top and bottom are no-ﬂow and no-heat ﬂux boundaries. The outer
boundary has a constant temperature, salt concentration and head
that equals the initial conditions. The Preconditioned Conjugate Gra-
dient 2 (PCG2) was used to solve for groundwater ﬂow. The method
of characteristics (MOC) was applied to solve the advection part of
transport, with a Courant number of 0.1. The convergence criterion of
relative temperature was set to 10−10 °C to simulate heat conduction
with a high bulk thermal diffusivity accurately .
2.4.1. Model parameters and sensitivity
First, the standard SEAWATv4 with a linear density relation was
applied and results for the reference scenario (Table 2) were com-
pared with the results from a simulation with the newly imple-
mented non-linear relation. Subsequently, the non-linear relation
was used for the subsequent simulations to investigate the sensitivity
of modeling results on the main input variables of well casing temper-
ature (Tc), salt concentration contrasts (Cs), as well as aquifer proper-
ties (Table 2). A non-linear density–temperature relation without the
density effects of salinity (see Eq. (8),S=0 kg/m3) was used for Case
3.3. The same conditions were assumed as for Case 3.1 with a tracer
concentration (Ctr) of 1.0 kg/m3to investigate the effect of small salt
concentration gradients on density-driven ﬂow and salt mass trans-
port. The values for aquifer properties were varied within the range
expected for sandy aquifers, using Bear  and Fitts  for hydraulic
conductivity and porosity, as well as Molz et al.  and the Engineer-
ing Toolbox  for thermal conductivity and heat capacity. Heteroge-
neous sandy aquifers with small clay layers could have elevated heat
capacities, since average clay heat capacity is 920 J/kg°C, which is
higher than the value of 800 J/kg°C used for sand. Therefore, a sce-
nario with a higher heat capacity of the aquifer than used for the
reference scenario was also considered (Case 6.2). For all scenarios,
the viscosity dependence on temperature is taken in account using
Eq. (6) in SEAWATv4.
Other hydraulic properties and thermal properties (Table 3) were
kept constant between the various simulations. A longitudinal dis-
Summary of the input parameters analyzed in the sensitivity analysis. Underlined values indicate a variation on the reference scenario (Case 1).
Case Variation Tc[°C] Cs[kg/m3]kh[m/d] kv[m/d] λs[W/m °C] cps [J/kg °C] θ[dimensionless]
1 (Ref.) 80 35 15 1.5 3 800 0.35
c40 35 15 1.5 3 800 0.35
c60 35 15 1.5 3 800 0.35
s100 35 15 1.5 3 800 0.35
s80 1 15 1.5 3 800 0.35
s80 10 15 1.5 3 800 0.35
s80 1 15 1.5 3 800 0.35
h80 35 5 0.5 3 800 0.35
h80 35 45 4.5 3 800 0.35
4.3 kv=5kre f
v80 35 15 7.5 3 800 0.35
s80 35 15 1.5 2 800 0.35
s80 35 15 1.5 4 800 0.35
6.1 cps =0.9cref
ps 80 35 15 1.5 3 720 0.35
6.2 cps =1.1cref
ps 80 35 15 1.5 3 880 0.35
7.1 θ=0.6θref 80 35 15 1.5 3 800 0.21
7.2 θ=1.2aθref 80 35 15 1.5 3 800 0.42
aFor Case 3.3, a non-linear density–temperature relation was used without taking in account the density effects of the tracer concentration (Ctr).
J.H. van Lopik et al. / Advances in Water Resources 86 (2015) 32–45 37
Hydraulic and thermal aquifer properties used for all simulations.
Properties Parameter value
Speciﬁc storage Ss=1Å10−4m−1
Solid phase density ρs=2650 kg/m3
Heat capacity of the ﬂuid cpf =4186 J/kg °C
Thermal conductivity of the ﬂuid λf=0.580 W/m °C
Molecular diffusion Dm=8.64Å10−5m2/d
Longitudinal dispersivity αl=0.5 m
Transversal dispersivity αT=0.05 m
persivity value (αl) of 0.5 m and a transverse dispersivity value (αT)
of 0.05 m were chosen, resulting in a grid Peclet number of 1 near the
wellbore. SEAWAT uses a single set of dispersivity values which are
applied to both heat and solute transport.
2.5. Metrics to quantify overall salinization and compare
The distribution of salt in the top of the aquifer (upper 25 m) was
used to quantify the salinization and to facilitate comparison of the
scenarios. Several metrics were deﬁned for this purpose.
2.5.1. Cumulative salt mass and its associated center of mass
The transport of salt was quantiﬁed using the cumulative amount
of salt mass in the upper 25 m of the aquifer and the associated cen-
ter of mass. The cumulative salt mass is calculated using a summa-
tion over the salt mass in each grid cell in the model domain (725
columns, 100 layers):
where MTis the cumulative salt mass (kg), rjis the radial distance at
column j(m), and zkis the depth at layer k(m). The following equa-
tions give the coordinates rcM and zcM (m) of the center of mass of the
salt mass MTfrom Eq. (9):
2.5.2. Maximum radius of salinization
We used the maximal radial extent of salt concentrations above
0.1 kg/m3(100 ppm) close to the top of the aquifer (Rmax at z=1 m) to
quantify the maximum spreading of salt mass in the lateral direction.
2.5.3. Dimensionless analysis of thermo-haline convection
A dimensionless analysis is applied on the cases in the sensitivity
analysis (Table 2) in order to characterize the buoyancy forces in our
system. Both the temperature and the salt concentration affect the
buoyancy term in the ﬂow equation .
To determine the ratio between the buoyancy tendency due to the
salt concentration contrast and the buoyancy tendency due to the
temperature contrast, the Turner, or buoyancy, number is used :
where 1ρTis the maximum change in ﬂuid density due to tempera-
ture (kg/m3) and 1ρsis the maximum change in ﬂuid density due to
solute concentration (kg/m3). The dimensionless sensitivity analysis
for all scenarios is listed in Table 4.
The maximum change in ﬂuid density due to temperature contrasts (1ρT), the maxi-
mum change in ﬂuid density due to salt concentration contrasts (1ρs) and the associ-
ated buoyancy number for each scenario.
Case Parameter 1ρT[kg/m3]1ρs[kg/m3]B[dimensionless]
1Ref 27.13 27.15 1.00
2.1 Tc=40 °C 6.71 27.15 4.05
2.2 Tc=60 °C 15.67 27.15 1.73
2.3 Tc=100 °C 40.63 27.15 0.67
3.1 Cs=1 kg/m327.13 7.76 0.29
3.2 Cs=10 kg/m327.13 0.785 0.03
4.1 kh=5 m/d 27.13 27.15 1.00
4.2 kh=45 m/d 27.13 27.15 1.00
4.3 kv=7.5 m/d 27.13 27.15 1.00
5.1 λs=2 W/m °C 27.13 27.15 1.00
5.2 λs=4 W/m °C 27.13 27.15 1.00
6.1 cps =720 J/kg °C 27.13 27.15 1.0 0
6.2 cps =880 J/kg °C 27.13 27.15 1.00
7.1 θ=0.21 27.13 27.15 1.00
7.2 θ=0.42 27.13 27.15 1.00
First, the results for the reference scenario simulated with both
the standard linear density equation of state and the newly imple-
mented non-linear one are presented. Subsequently, the results of the
sensitivity analysis (Table 2) are presented.
3.1. Reference scenario (Case 1)
In the reference scenario (Case 1), the effect of heat transfer from
a hot well casing with a constant effective temperature of 80 °C for
40 years is simulated for a condition of fresh (0 kg/m3) groundwater
overlying groundwater with a seawater salt concentration (35 kg/m3,
3.1.1. Predicted salinization with linear and non-linear density
equation of state
Case 1 is the simulation of the reference scenario with the non-
linear density equation (Eq. (8)). The results show that density-
driven upward groundwater ﬂow along the wellbore induced by heat
transfer from the well casing led to considerable salinization of the
initially fresh upper part of the aquifer after 30 years (Fig. 5). Two
distinct thermal convection cells developed: one in the dense, salt
water at the bottom of the aquifer and another one in the fresh water.
The radial extent of these convection cells increases over time due
to the continuous heat transfer from the well casing. After hot saline
groundwater reaches the top of the aquifer, it is transported laterally.
It then gradually cools down and dilutes by mixing with the cooler,
The total salt mass in the top 25 m appears to increase exponen-
tially with time until it reaches a linear trend after 30 years, with
a rate of ∼4000 kg/year (Fig. 6A). The distance of the center of salt
mass and the maximum lateral spreading of salinization (Rmax) show
a rapid initial increase after which the increase tapers down (Fig. 6B
Modeling of the reference scenario (Case 1) was also done at dif-
ferent grid size (dr =0.33 m by dz =0.33 m) for [0.5 <r<154] and
dr =1 m by dz =0.33 m for [154 <r<500] to investigate the im-
pact of grid resolution on the model results. The effects on the main
metrics to quantify overall salinization (Section 2.5) are small, result-
ing in error percentages of total cumulative salt mass and associated
center of mass in the range of 0.18–1.95% and 0.33–1.02% respectively.
Therefore, no further grid reﬁnement was done and the grid conﬁgu-
ration described in Section 2.4 and was used for all simulations.
Case 1.1 is the reference scenario simulated with a linear den-
sity equation. A δρ/δCgradient of 0.73 was used for the linear salt
38 J.H. van Lopik et al. /Advances in Water Resources 86 (2015) 32–45
Fig. 5. (A) Salt concentrations [kg/m3] and (B) temperature [°C] at t=30 years for the non-linear reference scenario (Case 1) with the Darcy velocity vectors. The dot shows the
center of mass of cumulative stored salt in the model domain above the line [0 <z<25 m] over time and the red line shows Rmax. (For interpretation of the references to color in
this ﬁgure legend, the reader is referred to the web version of this article.)
concentration–density relationship (Eq. (7)) and a dρ/dT gradient
of −0.434 for the linear density–temperature relationship (line 1.1,
Fig. 2). The results of this simulation reveal trends similar to those
of the non-linear equation (Fig. 6). However, the linear density equa-
tion results in signiﬁcant overestimation of the cumulative salt mass:
140,437 kg after 30 years instead of 70,867 kg (Fig. 6A). The relative
error percentage for the cumulative salt mass increases from 81%
after 5 years up to 103% after 40 years, respectively. Also the lat-
eral spreading in the top of the aquifer is signiﬁcantly overestimated
while using the linear density equation. For instance, the r-coordinate
of the center of mass and the maximum lateral spreading of saliniza-
tion after 30 years is respectively 66.1 m and 103.5 m in the linear
density case instead of 53.6 m and 78 m in the non-linear density case
(Fig. 6B and C). The average relative error percentages for r-coordinate
of the center of mass and Rmax are respectively 24% and 32%.
The observed overestimation can be explained by the differ-
ences in the developed density gradients between the two cases. At
the lower end of the groundwater temperature range, the density–
temperature gradient for the non-linear density function is signif-
icantly lower than for the linear density approximation (line 1.1,
Fig. 2). Consequently, the upward advective salt mass transport at
low temperature ranges are signiﬁcantly overestimated by the linear
case (Case 1.1). Therefore, the associated mobilization of salt water
occurs over a consistently larger radial distance from the wellbore. In
addition to differences in upward advective salt mass transport, dis-
crepancies in salt mass transport between the cases with linear and
non-linear density equation of state are affected by differences in salt
water mixing by dispersion at the fresh-salt water interface. Differ-
ent lateral transport lengths and ﬂow velocities along the fresh-salt
water interface lead to variable extents of dispersive salt mixing.
It should be noted that convection is determined by the overall
density distribution that is affected by both temperature and salt con-
centration contrasts. Thermal retardation plays an important role in
the difference between advective salt transport and heat transport
during thermo-haline convection . Salt mass is approximately
transported at the pore velocity (q/θ), while heat is retarded due to
thermal equilibration between the water and the solid grains (see
Eq. (4)). Note that the salt water front at Rmax has moved along both
borehole length and the top of the aquifer, while the heat front has
only moved along the top of the aquifer. Consequently, the thermal
front moves much slower laterally away from the wellbore in the top
of the aquifer than the salt front (as illustrated by Fig. 5). This means
that at larger radial distance the vertical stabilizing temperature gra-
dient on density decreases, and therefore the destabilizing gradient
of salt concentration on density increases. If this destabilizing gradi-
ent of salt concentration is high enough and the horizontal ﬂow ve-
locity is low enough, downward transport of salt mass occurs at Rmax
(Fig. 5A). The lower density-temperature gradient in the temperature
range of 15–20 °C for the non-linear density equation (Case 1) com-
pared to the linear density approximation (Case 1.1) (line 1.1, Fig. 2),
results in a faster destabilizing effect of the salt concentration gradi-
ent on water density at closer radial distances from the well for Case
1. Therefore, lateral transport of salt mass in the top of the aquifer
(Rmax) is overestimated for the linear density equation.
3.1.2. Reference scenario: breakthrough curves
Two observation points were added to the reference scenario
to illustrate how the salinization and heating of the groundwater
progress over time. Obs-1 is placed at a radial distance of 0.75 m from
the wellbore, at a depth of 25 m and Obs-2 at a radial distance of
40 m from the wellbore in the upper 1 m of the aquifer (see Fig. 5).
The upward transport of saline groundwater results in a progressively
increasing but slightly ﬂuctuating salt concentration in the vicinity
of the wellbore (Fig. 7A). The salt concentration over time in Obs-1
increases from 4.7 kg/m3(4700 ppm) after 1.5 years to 16.5 kg/m3
(16,500 ppm) after 40 years. The groundwater temperature in Obs-1
J.H. van Lopik et al. / Advances in Water Resources 86 (2015) 32–45 39
Fig. 6. (A) Cumulative salt mass, (B) associated center of mass and (C) the maximum
spreading of salt mass in the lateral direction, Rmax, in the upper half of the aquifer
[0 <r<500 m], [0 <z<25 m] for the non-linear density scenario (Case 1) and the
linear density scenario (Case 1.1). The relative error percentage between Case 1 and
Case 1.1 is used to quantify the overestimation of these parameters while using the
linear density equation.
reaches steady state in 1 year and remains constant at a temperature
of 70.5 °C (Fig. 7A). Consequently, the upward Darcy velocity in Obs-1
after 1.5 years is 0.059 m/day and decreases slightly due to the in-
creasing salt concentration and density of the groundwater (Fig. 8).
At a radial distance of 4.75 m, no elevated salt concentrations break-
through occurs and the upward Darcy velocity increases up to a value
of 0.011 m/day after 10 years in the fresh water layer. The strenght of
the lower salt water thermal convection cell is signiﬁcantly lower, re-
sulting in upward Darcy velocities which are a factor 0.52 lower than
observed in the fresh water layer at a radial distance of 4.75 m.
In the shallow observation point Obs-2 (Fig. 7B) elevated temper-
ature breakthrough occurs after 3.7 years, while elevated salt concen-
trations (at 0.1 kg/m3) breakthrough occurs after 6.7 years. In the ob-
servation point Obs-2, the salt concentrations vary strongly over time
between values of 2.00 (2000 ppm) and 2.45 kg/m3(2450 ppm) af-
ter 30 years. Moreover, the variability in salt concentrations increases
over time (Fig. 7B).
3.2. Parameter sensitivity analysis
Sensitivity analysis was conducted to test how the salinization is
affected by various factors. A set of 6 parameters was varied with re-
spect to the reference scenario which is shown in Table 2. Three dif-
ferent temperatures at the well casing (Case 2) were simulated, as
well as three different salt concentration contrasts with the overlying
fresh water (Case 3), two hydraulic conductivities (Case 4), two ther-
mal conductivities (Case 5), two solid phase heat capacities (Case 6),
and two porosities (Case 7).
3.2.1. Effect of well casing temperature (Case 2)
The well temperature at shallow depth can vary over a wide range,
depending on the technical application of the well as well as its pro-
duction depth and insulation. In the simulations, the rate of salt mass
transport and lateral spreading in the top of the aquifer were clearly
affected by different effective well casing temperatures (Fig. 9). The
highest casing temperatures resulted in the strongest increase in ver-
tical transport and lateral spreading of salt mass in the upper part
of the aquifer (Fig. 9). For a casing temperature of 100 °C (Case 2.3),
the temperature is high enough to overcome the density difference
between saline and fresh water (B=0.67, Table 4). Consequently, ad-
vective transport of salt mass was observed along the whole well-
bore length. This was not observed for Cases 1, 2.1 and 2.2, where the
buoyancy number B<1 (Table 4). The accumulation of transported
salt mass into the top of the aquifer is disproportionally large with
respect to the increases in effective temperature of the well casing.
For example, the increase of temperature from 40 to 60 °C yields a
6.2–9 fold increase in total salt mass transport over the whole time
range. In contrast, the lateral salt spreading increases progressively
less at higher well casing temperatures. Low well casing tempera-
tures (Tc=40 °C) already result in distinct lateral spreading of salt
mass in the top of the aquifer (Case 2.1) (Fig. 10).
3.2.2. Effect of salt concentration contrast (Case 3)
The reference scenario (Case 1) has fresh groundwater
(Cs=0 kg/m3) overlying water with a salt concentration of 35 kg/m3,
which is representative of intruding seawater in coastal areas (e.g.
). However, smaller salt concentration contrasts may be present,
e.g. due to long-term progressive salinization . Cases 3.1 and 3.2
have salt concentration contrasts of 1 and 10 kg/m3, respectively.
The rate of salt mass transport for Case 3.1 is only a factor 2.1 lower
than for Case 1, while for Case 3.2 it is approximately a factor 1.2
higher (Fig. 11A). Although salt mass transport is highest for a salt
concentration contrast of 10 kg/m3, the lateral spreading, as reﬂected
by the radial center of mass and Rmax, is slightly higher for the case
with a lower (1 kg/m3) salt concentration contrast (Fig. 11B and C).
Two convection cells developed in the reference scenario (Case
1). In contrast, upward convective ﬂow is not restricted at the fresh-
salt interface for Cases 3.1 and 3.2. The buoyancy numbers B for both
Cases 3.1 and 3.2 are lower than 1 (Table 4). Hence, the well casing
temperature of 80 °C is suﬃciently high to decrease the density of
the water with a salt concentration of 1 or 10 kg/m3below that of
the initially fresh water density at 15 °C in the vicinity of the well-
bore. Therefore, the saline groundwater moves upward over the en-
tire thickness of the aquifer (Fig. 12A).
The stabilizing effect of salt concentration on the density contrasts
is not taken into account for Case 3.3. The effect on the cumulative
salt mass transport is the same as for Case 3.1 (Fig. 11A). However,
lateral spreading of salt mass in the top of the aquifer was a factor
1.1 higher for Case 3.3 than for Case 3.1 (Figs. 11C and 12). Hence,
the destabelizing effect of the salt concentration on density contrasts
during lateral transport of salt mass in Case 3.1 results in a smaller
radial extent of the convection cell over time compared to Case 3.3.
3.2.3. Effect of hydraulic conductivity (Case 4)
The hydraulic conductivity of the aquifer inﬂuences groundwater
ﬂow velocities. Decreasing khand kvvalues by a factor of 3 (Case 4.1),
the cumulative salt mass transported into the top of aquifer decreases
40 J.H. van Lopik et al. /Advances in Water Resources 86 (2015) 32–45
Fig. 7. Breakthrough curves at observation points (A) Obs-1 and (B) Obs-2 for respectively salt concentration and temperature for the reference scenario (Case 1).
Fig. 8. Upward Darcy velocity over time at different radial distances in the vicinity of
the wellbore 25 m depth.
by a factor of 3.0 compared to the reference case (Fig. 13). The con-
trary is observed for Case 4.2, where khand kvare increased by a fac-
tor of 3. This results in increased cumulative salt mass in the top of
aquifer by a factor of 2.5. Case 4.3 has a higher anisotropy ratio, where
kvis raised to 7.5 m/day. This results in the largest salt mass trans-
ported into the top of the aquifer after 15 years of all considered sce-
narios. The downward transport of salt mass at the outer boundary
of the convection cell is also increased for both Cases 4.2 and 4.3 and
salt water is already transported to a depth below 25 m after 24 and
17 years, respectively. Consequently, continuous salt mass loss out of
the upper aquifer domain [0 <z<25 m] results in a slower increase
of cumulative salt mass for these cases (Fig. 13A and B).
3.2.4. Different thermal properties of the aquifer (Cases 5 and 6)
The thermal conductivity and heat capacity of the solid phase in-
ﬂuence heat transport via the bulk thermal diffusivity term (Eq. (3))
and the thermal retardation factor (Eq. (5)), respectively. A higher
thermal conductivity of the solid phase increases the heat conduction
from the well casing to the aquifer and the density-driven groundwa-
ter ﬂow. Varying the thermal conductivity for the solid phase within
Fig. 9. (A) Cumulative salt mass, (B) associated center of mass and (C) Rmax in the upper
half of the aquifer [0 <r<500 m], [0 <z<25 m] for Case 2.
J.H. van Lopik et al. / Advances in Water Resources 86 (2015) 32–45 41
Fig. 10. (A) Salt concentrations [kg/m3] and (B) temperature [°C] at t=30 years for the scenario with a well casing temperature of 40 °C (Case 2.1) with the Darcy velocity vectors.
The dot shows the center of mass of cumulative stored salt in the model domain above the line [0 <z<25 m] over time and the red line shows Rmax. (For interpretation of the
references to color in this ﬁgure legend, the reader is referred to the web version of this article.)
a realistic range showed a moderate impact on the convection. The
salt mass transported into the top of the aquifer increased by a factor
of 1.2 for the upper bound (Case 5.2) and decreased by a factor of 1.2
for the lower bound (Case 5.1) after 30 years (Fig. 13).
Besides thermal conduction, heat transport is determined by ther-
mal retardation which is described as a function of the heat capacity
of the solid (Eq. (5)). The effect of thermal retardation is small (Case
6). A higher heat capacity of the solid (Case 6.2) resulted in more
absorption of heat into the solid matrix during heat transport and
thereby a higher thermal retardation factor. Consequently, the salt
front moves faster laterally away from the well than the thermal front
and cooling of the salt front occurs at closer radial distances from the
well. This results in a faster destabilizing effect of the salt concentra-
tion gradient on water density during lateral salt transport and hence
a reduced maximal lateral spreading (Rmax). The reverse is observed
for Case 6.1, since the adsorption of heat into the solid matrix is lower
than the reference scenario.
3.2.5. Effect of aquifer porosity (Case 7)
Porosity affects heat transport by bulk thermal diffusivity (Eq. (3))
and thermal retardation (Eq. (5)). SEAWATv4 allows only modeling
with effective porosity, while heat conduction is determined by the
overall, bulk porosity. Hence, thermal conduction in the aquifer will
be slightly overestimated when considering effective porosity instead
of bulk porosity, since the bulk thermal diffusivity term (DT) will be
lower in the simulations. The total cumulative salt mass in the top
of the aquifer for Case 7 indicates that the parameter sensitivity for
varying porosity is high (Fig. 13). The lowering of the porosity by a
factor of 0.6 (Case 7.1) increased the salt mass transport by a factor
of 1.14. An increased porosity by a factor 1.2 results in decreased salt
mass transport by a factor of 1.04. The decrease and increase in salt
mass transport are mainly due to the difference in advective salt mass
transport. For Case 7.1, the pore velocity (q/θ) at a given Darcy velocity
is increased by a factor 1.7, while for Case 7.2 the pore velocity is de-
creased by a factor 1.2. In reality such porosity changes would likely
be accompanied by permeability changes that mitigate the impact of
Simulations show that the heat loss from well casings can induce
upward convection of salty groundwater, leading to salinization of
overlying fresh groundwater. To the best of our knowledge, this is the
ﬁrst study that considers the impact of hot well casings on groundwa-
ter ﬂow and salt concentration gradients in aquifers. Here, the prac-
tical implications, such as monitoring requirements and the impli-
cations of modeling density-driven ﬂow under the conditions pre-
sented in this study will be discussed.
4.1. Implementation of non-linear density equation of state
We have simulated density-driven ﬂow over large temperature
and salt concentration ranges induced by the heat transfer from a hot
well casing. The resulting salt and heat transport in the aquifer was
shown to occur over relatively short distances (<100 m). The imple-
mentation of a non-linear density equation of state  in SEAWAT
was required for accurate results, as the linear approximation causes
relative errors up to 103% for the cumulative salt mass transport.
Other numerical simulations of convection induced by temperature
gradients use a non-linear relation between density and temperature
only (e.g. [15,42]). This study uses a non-linear density dependence
on both salt concentration and temperature.
Generally, heat transport mechanisms are classiﬁed as natural
(free) convection if ﬂow is solely induced by ﬂuid density differences
and forced convection if ﬂow is forced by external sources, like a
hydraulic gradient. Previous studies have shown that heat transport
42 J.H. van Lopik et al. /Advances in Water Resources 86 (2015) 32–45
Fig. 11. (A) Cumulative salt mass, (B) associated center of mass and (C) Rmax in the
upper half of the aquifer [0 <r<500 m], [0 <z<25 m] for Case 3.
by forced convection over relative small time ranges can be simu-
lated with linear density approximations in the SEAWAT code (e.g.
[25,44]). However, in the present study, heat transport is solely due
to free convection under the inﬂuence of continuous heat conduction
from the well casing over a large time range (up to 40 years). The
radial temperature distribution in the model domain varies spatially
and temporally. No sharp temperature front between the hot water
mass and colder ambient groundwater is observed (shown in Fig. 5B).
Both temperature and salt concentration distributions determine the
extent of the convection cells and the associated convective transport
over time. This is reﬂected in the difference between the simulations
with linear and non-linear density relations (Fig. 6).
A non-linear density relation in SEAWAT enables numerical sim-
ulations of problems where thermally induced free convection in
aquifers occurs over large temperature and time ranges. A disadvan-
tage would be the increased run times associated with the use of a
non-linear density relation. The higher accuracy of the implemented
non-linear density equation comes at the price of a larger compu-
tational runtime: 50 h compared to 20 for Case 1.1 with a Core i7-
firstname.lastname@example.org GHz processor.
4.2. Well casing temperatures of exploration wells
The range of well casing temperatures used in this study is repre-
sentative for temperatures encountered for conventional oil and gas
wells, geothermal energy production, as well as hot water or steam
injection [6,11,13,35,50]. However, little information is available on
the actual temperature at the outside of the well casing. The actual
temperature is an important parameter changing for different practi-
cal applications. This means that for a speciﬁc production or injection
operation detailed information about the wellhead temperature over
depth, the thermal resistance of the well system and the actual tem-
perature gradient over time in the well system is required to simulate
heat transfer into the aquifer as accurately as possible.
Decline in production rates results in decreasing well casing tem-
peratures. Therefore, the effects of thermally induced density-driven
groundwater ﬂow on upward salt transport are expected to be lower
when the duration of heat transfer through the wellbore decreases to
a few years. For example, typical initial shale gas production rates of
major U.S. shale gas ﬁelds are around 30 million m3per year, while
production rates drops to values around 4 million m3per year af-
ter 5 years of operation . The analytical function by Ramey 
predicts that such low production rates will result in small tempera-
ture differences (<5°C) between the wellbore ﬂuid and the shallow
4.3. Fresh-salt interfaces and salt concentration contrasts
Fresh-salt interfaces are common in coastal areas (e.g. ). In
general, these interfaces have relative small dispersed transition
zones between fresh and saline waters compared to other stratiﬁed
fresh-salt aquifer systems. Usually, coastal regions are densely popu-
lated and fresh water reserves are scarce. Salinization poses problems
for drinking water, agriculture, and ecological habitats [34,48]. This
study can be used to provide insight into possible thermal impacts
on groundwater ﬂow and salinization risks near deep wells penetrat-
ing fresh water lenses.
Fresh-salt groundwater stratiﬁcation also occurs in regions with
brackish paleo-groundwater, or halite-rich formations [5,33]. For
these scenarios, the lower salt concentration contrasts of 1 and
10 kg/m3(Cases 3.1 and 3.2) are realistic. However, a less sharp dis-
persed fresh-salt transition should be considered under these condi-
tions . Salt mass transport from the upper part of the diffusive
transition zone could then occur at lower temperature contrasts. For
example, for Case 3.2, the salt concentrations in the upper part of a
diffusive transition interface will be lower compared to a case with a
sharp salt concentration contrast of 10 kg/m3. Consequently, the re-
quired temperature rise to overcome the buoyancy difference with
cold fresh groundwater will be lower. Therefore, it is likely that salt
transport occurs over a larger radial distance along the wellbore if a
wide diffusive fresh-salt transition zone is considered.
Moreover, direct upward salt transport over the entire aquifer
thickness occurs for the lower salt concentration contrasts (1 and
10 kg/m3) of Cases 3.1 and 3.2 (Section 3.2.2). The density difference
for the reference scenario is too large to allow direct groundwater
ﬂow along whole borehole length at the simulated effective well cas-
ing temperatures (Cases 1 and 2.1–2.3). Consequently, the effect of
salt mixing by dispersion between the salt and fresh water layer along
the fresh-salt interface becomes more important for this case with
two separate convection cells.
4.4. Uncertainties in the simulation results
Dispersion along the fresh-salt interface controls the salt trans-
port to the top of the aquifer for large salt concentration contrasts
when two convection cells develop (e.g. Case 1). Such enhanced salt
water mixing along a fresh-salt water interface due to the formation
of thermal convection cells was observed in the lab experiment of
Henry and Hilleke  and numerical simulations of this experiment
. In this experiment, warm fresh water was injected in a large
sand-ﬁlled tank and ﬂowed on top of water with a salt concentration
of 35 kg/m3. Heat pads were located at the lower and right part of the
J.H. van Lopik et al. / Advances in Water Resources 86 (2015) 32–45 43
Fig. 12. (A) Salt concentrations [kg/m3] for Case 3.1 and (B) salt concentrations [kg/m3] for Case 3.3 at t=30 years with the Darcy velocity vectors. The dots show the center of
mass of cumulative stored salt in the model domain above the line [0 <z<25 m] over time and the red line shows Rmax. (For interpretation of the references to color in this ﬁgure
legend, the reader is referred to the web version of this article.)
Fig. 13. Sensitivity of the (A) cumulative salt mass, (B) associated center of mass, and
(C) Rmax in the upper half of the aquifer [0 <r<500 m], [0 <z<25 m] after 15 and 30
years. ∗Note that for Cases 4.2 and 4.3 salt has been transported downward, below the
25 m reference line at the outside of the convection cell.
sand-ﬁlled tank, resulting in thermal convection cells in the lower left
part of the tank in both the fresh and the salt water layer. The mix-
ing by these convection cells widened the fresh-salt interface. For a
simulation scenario without taking into account the temperature de-
pendency of the density, less salt mass transport was observed due to
the absence of thermal convection cells.
This illustrates that the mixing along a fresh-salt interface is
largely controlled by advection and transverse dispersion [4,31]. The
presented simulations used dispersivity values of αl=0.5 m and
αT=0.05 m. Enhanced solute mixing by dispersion will result in in-
creased salt mass transport to the top of the aquifer. For example, a
scenario with dispersivity values of αl=1.0 m and αT=0.1 m re-
sulted in an increase in salt mass transport by a factor of 1.14. There-
fore, the dispersivity value should be carefully considered for simula-
tions of speciﬁc ﬁeld cases with fresh-salt interfaces (e.g. ).
Small ﬂuctuations of salt concentrations with time are observed
in the vicinity of the wellbore, when the salt concentration contrast
of the interface is large (such as in Case 1, Fig. 7A). This can be ex-
plained by the difference in diffusivity between heat and salt. The
initial situation is stable due to the salt concentration gradient. The
heat transfer from the wellbore causes destabilization of the system.
This is called the diffusive regime of Double Diffusive Convection and
instabilities can arise during this phenomenon . At the top, hot salt
water moves laterally over colder fresh water. This is called the ﬁn-
gering regime of Double Diffusive Convection [4,17,39]. If the desta-
bilizing salt concentration gradient in the top of the aquifer is large
(e.g. Case 1 and Case 3.2), it results in instabilities and ﬂuctuating
salt concentrations over time (Fig. 7B). The salt concentration ﬂuctu-
ations due to Double Diffusive Convection decreases with enhanced
salt mixing by dispersion.
Grid resolution, dispersivity values, and the use of a 2D axi-
symmetric domain could have an effect on the simulation of unsta-
ble upward ﬂuid ﬂow along the wellbore and local salt concentration
ﬂuctuations (e.g. [4,19]). Therefore, the salt concentrations should be
44 J.H. van Lopik et al. /Advances in Water Resources 86 (2015) 32–45
measured frequently in the ﬁeld (e.g. using automatic electrical con-
ductivity (EC) data loggers) to obtain insight in the mixing and the
average salt concentrations at the top of the aquifer.
This study did not consider heat loss from the aquifer into the
conﬁning layers. Horizontal heat transport from hot well casings
to surrounding aquitards will be conduction dominated, while heat
transport in the aquifer occurs by both conduction and convection.
As illustrated in Fig. 5B, the upward convective heat transport results
in heat accumulation and hence a larger radius of elevated aquifer
temperature at the top of the aquifer. The radius of elevated aquifer
temperature at the bottom of the aquifer is reduced by the convec-
tive inﬂow of cooler native groundwater. Heat conduction into and
from the aquifer can be expected for the underlying and overlying
aquitards, respectively. However, the thermal conductivity is gener-
ally high for clay layers compared to the thermal conductivity of
sandy aquifers [1,7]. Hence, heat transfer from the well casing into
the aquitard by thermal conduction is expected to be higher than for
the aquifer. Therefore, heat conduction into the aquitard is expected
to have a limited impact on the lateral transport of salt in the top of
4.5. Practical considerations
The present study shows the possibility of signiﬁcant upward
transport of salt around hot well casings. Field evidence of this phe-
nomenon does not exist to the best of our knowledge. This would re-
quire spatially detailed and frequent long-term monitoring to obtain
quantitative insight on such thermo-haline convection in the vicinity
of hot wells. The simulations of the present study were carried out for
an axi-symmetric homogeneous sandy conﬁned aquifer domain. This
section addresses the implications of different ﬁeld conditions.
Axi-symmetric ﬂow condition strongly reduces simulation run-
ning times, but does not allow simulation of regional groundwater
ﬂow. However, regional ﬂow will increase the net heat transfer from
the hot well casing to ambient groundwater and cause a different
temperature distribution around the well. This will change the ther-
mal convection cells in both salt and fresh water layer.
The aquifer was assumed to be homogeneous. However, variations
in hydraulic and thermal properties of the aquifer near the wellbore
would impact the density-driven groundwater ﬂow and salt mass
transport. Aquifer heterogeneity could have a large impact on con-
vective ﬂow patterns in thermo-haline systems . For example,
horizontal clay lenses restrict density-driven ﬂow and may lead to
separate convection cells above and below a clay lens. Consequently,
salinization of the upper part of the aquifer might be limited or even
Unconﬁned aquifers were not tested in this study. For an uncon-
ﬁned aquifer, the temperature at the water table is controlled by the
atmospheric temperature. Continuous heat loss at the top results in
less intensive convection. Consequently, salt mass transport and lat-
eral spreading of salt in the top of the phreatic zone are expected to
be lower as for conﬁned aquifers. In addition, unconﬁned aquifers are
recharged with fresh water by precipitation which will dilute trans-
ported salt water in the top of the phreatic zone.
To the best of our knowledge, this is the ﬁrst study that shows that
heat loss from well casings may cause mixing due to density-driven
ﬂow and mobilize fresh-salt water interfaces, resulting in salinization
of shallow fresh groundwater. A non-linear density relationship as a
function of both salt concentration and temperature had to be imple-
mented in the SEAWATv4 code to simulate this phenomenon accu-
rately. The total transported salt mass to the top of the aquifer ranged
between values of 3150 and 166,000 kg after 30 years for the simu-
lated scenarios. Lateral spreading of salt mass in the top of the aquifer
occurred over radial distances up to 91 m. During lateral transport of
salt water along the top of the aquifer, ﬂuctuating salt concentration
breakthrough over time occurs due to destabilizing salt concentration
For large salt concentration contrasts, such as a fresh-salt (seawa-
ter) interface, groundwater heating results in the formation of sepa-
rate convection cells in the fresh water layer and the salt water layer.
At smaller salt concentration contrasts, the heated salt water layer
becomes less dense than the cooler native groundwater. Hence, up-
ward advective transport of salt along the wellbore occurs over the
entire thickness of the aquifer.
The convection and salt transport is stronger for scenarios with
increased temperatures of the well casing, increased horizontal and
vertical hydraulic conductivities, decreased porosity and increased
thermal conductivity of the aquifer. Therefore, these aspects should
be considered when assessing the potential impact of hot well casings
for site-speciﬁc conditions. The results of this study indicate heat loss
from hot well casings can induce density-driven groundwater ﬂow
and salinization of shallow fresh groundwater. This process should
therefore be considered when monitoring for long-term groundwa-
ter quality changes near wells through which hot ﬂuids or gases are
The authors thank four anonymous reviewers for their con-
structive feedback, which allowed us to improve the manuscript
Appendix A. Modiﬁed density equation in SEAWAT
The calculation steps for the density calculation (Fig. 4) are out-
lined in this appendix. The non-linear density equation (Eq. (8)) has
been implemented in the VDF package of SEAWAT. The code for the
function CALCDENS in the VFD1.f ﬁle has been adapted. This function
calculates ﬂuid density for each grid cell from the concentrations of
each MT3DMS species, which is in our model salt concentration (Cs)
and temperature (T).
First the salt concentration (in kg/m3) and temperature (in °C) are
read. Subsequently, the iterative algorithm is performed by solving
ρn=(999.9+2.034 ·10−2T−6.162 ·10−3T2
+2.261 ·10−5T3−4.657 ·10−8T4)
1000 −2.001 S
1000 T+1.677 ·10−2S
1000 T3−1.613 ·10−5S
Closure of the iterative scheme is set to residual rρ<1−10−3.
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