Solar pond technology for large-scale heat processing in a Chilean mine

F. Garrido, R. Soto, J. Vergara, M. Walczak, P. Kanehl, R. Nel, and J. García

Citation: Journal of Renewable and Sustainable Energy 4, 053115 (2012); doi: 10.1063/1.4757627
View online: http://dx.doi.org/10.1063/1.4757627
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 JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 4, 053115 (2012)

Solar pond technology for large-scale heat processing

in a Chilean mine
F. Garrido,1 R. Soto,1 J. Vergara,1,a) M. Walczak,1 P. Kanehl,2 R. Nel,3
and J. Garcıa4
1
Department of Mechanical and Metallurgical Engineering, Pontificia Universidad Cat
olica
de Chile, Santiago, Chile
2
Department of Mechanical Engineering and Transport Systems, Technische Universit€at
Berlin, Berlin, Germany
3
Stellenbosch University, Stellenbosch, South Africa
4
JHG Ingenierıa Ltda., Santiago, Chile
(Received 9 May 2012; accepted 14 September 2012; published online 4 October 2012)

Copper mining is the largest industrial activity in Northern Chile, a region that
relies mostly on imported energy resources thus making the mining sector
vulnerable to the rising cost of fuel oil and electricity. The extraction of copper is
mostly accomplished by hydrometallurgy, a three-step low energy process
consisting of heap leaching, concentration by solvent extraction, and metal
recovery by electro-winning. Since the content of copper in its ore tends to degrade
as the mining operation proceeds, higher leaching temperatures would be needed
along with increasing energy requirements. In order to address this demand and
considering that the region has one of the highest levels of solar radiation and clear
skies, the authors assessed the solar pond technology for rising the temperature of
the leaching stream. The working principle of such technology is presented, as well
as its mathematical formulation, restrictions, and assumptions, aiming to simulate
the performance of a solar pond and to size a suitable setup. The results indicate
that this technology can provide sufficient heat to raise the temperature to a range
of 50 to 70  C throughout the year with an annual gross thermal supply of
626 GWh. In order to minimize the loss of water and salt from the pond, a closed
salt cycle is suggested. Savings of up to 59 000 tons of diesel oil per year and the
avoidance of 164 000 tons of CO2 per year could be achieved with a solar pond
effective area of 1.43 km2 reaching an average efficiency of 19.4%. Thus, solar
pond technology is suitable for attaining the goal of increasing the leaching
temperature while diminishing fuel costs and greenhouse emissions. V C 2012

American Institute of Physics. [http://dx.doi.org/10.1063/1.4757627]

I. INTRODUCTION
Copper is present in nature mainly in the form of copper sulfide. Nearly 80% of the copper
produced in the world is obtained from sulfide ores by means of pyrometallurgy, a process
entailing concentration, smelting, and refining.1 The remaining 20% is obtained from copper
oxides by hydrometallurgy in which the crushed ore is piled in large heaps and leached with an
aqueous-acid mixture. The pregnant solution is then transported to solvent-extraction (SX)
where by means of chemical extractants an organic phase rich in copper is separated from the
depleted aqueous phase. The copper-laden phase is then converted back to aqueous from which
metallic copper is obtained in the process of electro-winning (EW). Here, an electrical potential
is applied between an inert anode and a cathode on which copper from the electrolyte is plated
with the purity greater than 99.8%. The cathode is then striped and the copper shipped to the

a)
Author to whom correspondence should be addressed. Electronic mail: jvergara@ing.puc.cl.

1941-7012/2012/4(5)/053115/17/$30.00 4, 053115-1 C 2012 American Institute of Physics

V

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 053115-2 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

market. This extractive method was first implemented in 1970, but only in the 1990s, it became
economically viable. For its low capital and operational costs, it has gained interest especially
in Chile2 with the results of 66% of the copper obtained by hydrometallurgy in the world being
produced in Chile in 2010.3
The vast majority of the mining operations in Chile are located in the Atacama Desert.
These mining sites contributed in 2010 around 70% of the total copper produced in the
country,4 which corresponds with 24% of the global production.5 This region also has a high
potential for deploying solar energy. The average of 330 sunny days per year and an insolation
of 26 MJ/m2per day (measurements carried out by JHG Ingenierıa Ltda. throughout year
2009) combined with aridness in uninhabited zones provide plenty of space for accommodating
solar energy technologies.
In the last decade, renewable energies have gained interest and experienced a significant
development as environmentally friendly alternatives to traditional energy sources, such as coal,
gas, or oil. The main motivation is the commitment of individual countries to reduce their
greenhouse gas emissions and also to reduce their energy dependence. In this context, solar
ponds appear as an attractive method to produce and supply the heat necessary for mineral
processing in any processing site situated similarly to the North of Chile.
Solar ponds represent a type of renewable energy suitable for applications requiring low
temperature heat.6,7 A solar pond (Figure 1) consists basically in a body of salty water that col-
lects and stores the incident solar radiation in the form of heat which can be further extracted
for practical use. In order to prevent the convection currents produced by the buoyancy of the
hot water, a density gradient is developed using high concentrations of salt at the bottom of the
pond (20–30 wt. %), to almost zero in the top layer.8 This gradient acts as a transparent insula-
tor that allows the solar radiation to be “trapped” below. A typical solar pond consists of three
zones: the upper convective zone (UCZ) composed by low salinity brine at ambient tempera-
ture, a non-convective zone (NCZ) where the concentration gradient is found, and the lower
convective zone (LCZ) where the heat is stored and from where it can be withdrawn.9 Temper-
ature, salinity, and density of UCZ and LCZ are kept almost constant, while in the NCZ, all
these quantities increase with depth. Since no heat emerges to the surface, the system serves for
both heat production and thermal storage.
Maintaining stability of the salt gradient is essential for the correct operation of a pond.
The fact that the salt concentration of a solar pond increases with depth implies diffusion of
salt in the opposite direction (from bottom to the top). The rate of the diffusion process is
determined by molecular diffusivity of the salt, gradient of salt concentration, and induced
mass eddy diffusivity caused by surface waves or other perturbations.10 The mass diffusion of
salt shatters the density gradient, which over a period of time could lose the heat from the bot-
tom to the atmosphere due to the now possible convection.9 In order to maintain the required
salt gradient profile, the LCZ has to be replenished with salt, while the slightly saline water of
the pond’s surface has to be replaced by fresh water. If the amount of salt equivalent to the dif-
fused quantity is not added to the pond, the salinity in the bottom region will decrease causing

FIG. 1. Working principle of solar pond technology.

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a density gradient in the insulating layer to destabilize the pond.11 As long as the stability of
the gradient is preserved, the stored heat is available throughout the entire day and night.
To make use of the heat stored in the LCZ, two techniques are commonly used. The first
one consists of a heat extraction system submerged in the LCZ. The heat-exchange fluid is
pumped to a secondary heat exchanger outside the pond in order to transfer its thermal energy.
The main disadvantages of this technique are the large amount of pipework involved, difficul-
ties in maintenance of the system, and risk of corrosion due to the aggressive environment.7
The alternative is to extract the hot brine from the LCZ by means of diffusers, circulate it
through an external heat exchanger, and then return it to the pond. If the brine is re-injected at
the bottom, the heat losses through the ground are reduced.12 Also, the velocity of the horizon-
tal flow produced by the brine extraction and re-injection into the LCZ are small enough to pre-
vent erosion in the gradient zone.13
Thermal efficiency of a solar pond is defined as the fraction of the solar radiation incident
on the surface of the pond that is absorbed in the LCZ.6 Values of 10% to 30% are possible to
achieve depending on the thickness of the three zones as well as the storage temperature which
ranges typically from 40 to 80  C.
The earliest records of solar ponds were obtained through observations of natural phenom-
ena. The first natural solar lake was recorded in the Medve Lake in Transylvania (Hungary),
where temperatures of up to 70  C were detected at the bottom of the lake, which was appa-
rently caused by salt and a salinity gradient in the lake.14 Similar observations were made in
other saline lakes such as Lake Vanda and Lake Bonney in Antarctica and Castle Lake in
California.15
This thermal phenomenon found in saline lakes led Dr. Rudolph Bloch, in 1954, to develop
the idea of collecting solar energy by creating artificial solar ponds. The mathematical formula-
tion of a solar pond was first investigated by Weinberger.16 In 1975, Rabl and Nielsen17 devel-
oped the one-zone model of Weinberger into a two-zone pond.18 In 1981, Akbarzadeh and
Ahmadi10 studied the attenuation of solar radiation in a solar pond caused by salt concentration,
radiation propagation, and bottom and wall reflection. In 1984, Kishore and Joshi19 reported on
the heat losses from the pond to the ambient. Modeling of heat and salt diffusion as well as nu-
merical solution of the energy balance were investigated by Hull,20 Rubin et al.,21 Liao,22 Dah
et al.,23 Karim et al.,24 and other authors.25
In order to gather a better understanding of the thermal phenomena, construction of experi-
mental solar ponds has been realized in a number of countries, including Australia, India, Can-
ada, Portugal, former USSR, Kuwait, Turkey, and USA.15 Up to now, around 60 systems have
been constructed around the world, with surface areas ranging from a few hundred to a few
thousand square meters and they have been used for applications such as greenhouse heating,
process heat in dairy plants and other agricultural applications, desalination, and power
generation.6
One of the oldest and largest operational solar pond projects has been the El Paso solar
pond, operated by the University of Texas at El Paso through 16 years. The 3000 m2 pond
developed its gradient by sodium chloride and reached temperatures between 70 and 90  C. It
was used for desalination, processing of waste brine, production of industrial process heat, and
generation of electricity.12 A more recent project of similar size, called Pyramid Hill Solar
Pond, was constructed in 2000 in northern Victoria in Australia by RMIT University in partner-
ship with two Australian companies. It has been used for industrial process heating with tem-
peratures between 50 and 80  C. The heat has been used in high-grade salt production (includ-
ing commercial salt production), aquaculture, and in demonstrative inland desalination.12 The
biggest project until now, called The Beith Ha’Arava plant, was constructed in Israel in 1958
and operated until 1988 with a total surface of 250 000 m2. It was capable of producing an
electric power of 5 MW using an organic Rankine cycle.26
The aim of this work is to evaluate the suitability of implementing solar pond technology
and its performance to supply a large scale and constant demand of energy equivalent to 613
200 MWh of process heat with an intermittent source such as solar energy. This heat is
required to increase the temperature of water by 25  C from ambient temperature and is to be

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 053115-4 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

used for copper leaching in a mining site located in the North of Chile (Atacama Desert),
200 km South-East from the coastal city of Antofagasta and 3100 m above the sea level.

II. METHODOLOGY
To carry out this study, a theoretical analysis of solar ponds was chosen. From literature
review, different models describing certain aspects of the behavior of solar ponds were studied,
integrated, and validated. The model of pond’s thermal behavior proposed by Jaefarzadeh18 was
adopted along with pond’s dynamics derived from Navier-Stokes balance equations, whereas
the works of Akbarzadeh and Ahmadi,10 Hull et al.,27 and Kishore and Joshi19 were used to es-
tablish boundary conditions. Furthermore, double diffusivity, boundary behavior in the layer-
layer, layer-bottom and layer-atmosphere interfaces, one-dimensional stability, as well as heat
extraction from the LCZ were considered. A computer program solving the analytical model
using finite differences was developed using MATLAB and validated against literature data
obtained from operational experience of a solar pond built at Los Alamos National Laboratory,
New Mexico, USA.28

III. MATHEMATICAL FORMULATION

Figure 1 shows the basic principle of a solar pond. Information about radiation reaching
the surface of the pond and its refraction, transmission, attenuation, reflection, and absorption
factors were used to calculate the energy absorbed within the individual layers. The absorbed
energy is part of the balance equations, which predict the dynamic temperature distribution in
the pond.

A. Insolation and absorption

The energy arriving to pond’s surface, due entirely to insolation, can be diminished by var-
ious atmospheric factors reducing the amount of solar radiation that can be transformed into
useful heat.
Solar radiation passing directly to Earth’s surface is referred to as direct solar radiation,
while the radiation that has been scattered out of the direct beam is referred to as diffuse solar
radiation. Scattering occurs when solar radiation is diffused in random directions due to an
interaction with gases or small particles, suspended in the atmosphere. The sum of both direct
and diffuse radiation over a horizontal surface constitutes the global solar radiation that can be
absorbed and finally stored in the lower convective layer of a salt gradient solar pond.
The energy absorbed in the pond, QI, was calculated by Eq. (1) according to the model
developed by Jaefarzadeh18
 
d Ae þ Ash n
QI ¼  Iðz; tÞ ; (1)
dz A

where I(z,t) is the direct radiation flux at depth z and time t, A is the total area of pond’s sur-
face, Ae is the sunny or effective radiation area, Ash is the shaded area and n is the fraction of
the direct radiation that becomes diffuse due to the shaded area.
The effective energy transmitted at the surface as well as the fractions absorbed by the dif-
ferent layers were estimated by Eq. (2)

X
4  
0 lj z
Iðz; tÞ ¼ ð1  RÞh cos #i I0 gj exp ; (2)
j¼1
cos #r

where R is the reflectivity as a function of incident angle #i and refraction angle #r ,29 and h0 is
the reduction of solar radiation caused by presence of salt, internal scattering related to propa-
gation of light through the medium and reflectivity of side walls, I0 is the incident solar

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 053115-5 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

radiation, whereas the constants lj and gj estimate the absorption coefficients for the four main
wavelength spectra of solar radiation according to the model of Rabl and Nielsen.17

B. Fluid dynamics
Heat convection within the fluid determines the non-diffusive fluid motion and constitutes
the main contributor to heat and mass transfer. In a reposing fluid, convection is driven by local
changes of density, which are caused by changes in heat content or salinity. Since the salinity
rich water is heavier than fresh water, gravity becomes a factor resulting in the phenomenon
known as salt-finger. On the other hand, increased temperature has the opposite effect on den-
sity, thus increasing salinity, which in turn increases density, can compensate for convection
due to higher temperatures.
The change in density q is evaluated by Eq. (3) following a linear model:

dq ¼ qadT  qbdS; (3)

where T is the temperature and S is the salinity. a is the thermal expansion coefficient, given
by Eq. (4)

1 @q 
a¼  : (4)
q @T S

The salinity expansion coefficient b is given by Eq. (5)

1 @q 
b¼  : (5)
q @S T

In order to maintain a non-convective layer, the density changes caused by increased tempera-
ture in the vertical direction must not exceed those caused by salinity resulting in the condition
given by Eq. (6)
 
dT b @S
< : (6)
dz a @z

Equations of energy balance within the different layers of concentration gradient as well as sin-
gular boundary conditions at the bottom and sides of the pond can be used for predicting the
dynamic temperature distribution; therefore Navier-Stokes equations for incompressible fluids
in 3 dimensions can be utilized. There are 6 balance equations, which can be solved numeri-
cally. The differential form of the general balance equation for an arbitrary physical quantity /,
considering components of convection and conduction fluid flow, is given by Eq. (7)

@ @ @
ðq/Þþ ðqui /Þ þ ðcÞ ¼ S/ ; (7)
@t @xi @xi

where S/ represent external source of / and c is the non-convective flow. Equation (7) can be
used to obtain the desired balance equations by replacing / with the relevant physical
quantities.
The continuity equation or mass conservation in solar pond, where brine solution is
assumed to be incompressible, can be reduced to Eq. (8)

@ui
¼ 0: (8)
@xi

Further, conservation of momentum is described by Eq. (9)

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 053115-6 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

   
@uj @uj 1 @ @uj @p
þ uj ¼ l  þgj ; (9)
@t @xi q @xi @xi @xi

where l is the fluid’s viscosity, p is the pressure and gj is the external acceleration.
Conservation of energy for ideal fluid, including Fourier’s law, is described by Eq. (10)
 
@T @T @ @T @ui @IR
qc þ qui c ¼ K þ rij þ ; (10)
@t @xi @xi @xi @xj @x3

where K is the coefficient of heat conduction, c is the specific heat capacity, and IR is the total
solar radiation. Due to salinity of the pond, an additional equation has to be considered, because
vertical motion caused by convection can destroy the temperature profile and hence functional-
ity of the entire solar pond. In order to express the conservation of salinity (S), Eq. (7) was
considered for S, resulting in Eq. (11)
 
@S @S @ @S
q þ qui ¼ Dq þ si  s0 ; (11)
@t @xi @xi @xi

where si represents the incoming salt of make-up brine per unit of time required to maintain the
salt profile and so is the loss due to evaporation per unit of time.

C. Heat extraction
The heat exchanger is submerged within the lower convective zone, where heat is trans-
ferred from the hot brine in the storage zone to the cold water circulating in the heat exchanger
tubes. The relation of Eq. (12) is valid for the rate of heat transfer30

Q_ ¼ ½mcðT
_ out  Tin Þwater ; (12)

where m _ is the mass flow rate of the fluid circulating in the exchanger tubes, c is the average
specific heat capacity of the fluid, whereas Tin and Tout are the inlet and outlet temperatures of
the heat exchanger tubes, respectively.
The required heat exchanger area can be obtained by Eq. (13)
 
TS  Tout
ln _
mc
TS  Tin
AS ¼  ; (13)
h
where Ts is the temperature of the surface of the tubes that compose the heat extraction system,
h is the heat transfer coefficient dependent on the thermal entry length and thus on the Reyn-
olds number of the water stream.
The rate of heat transfer from LCZ to the heat exchanger can be calculated using Eq. (14)
  
_Q ¼ NWSp qcðTLCZ  Tin Þ 1  exp  hpL ; (14)
WSp qc

where W is the velocity of the water, N is the total number of tubes, L is the length of a single
tube, p is the cross section perimeter of the pipe, and Sp is the cross section area of the tubes
that compose the heat extraction system. Note that m _ ¼ NWSp q and therefore the water flow in
_
each tube is mN ¼ WS p q.
Finally, the outlet temperature of the heat exchanger tubes was determined by Eq. (15)
 
hpL
Tout ¼ TðL=WÞ ¼ TLCZ  ðTLCZ  Tin Þexp  : (15)
WSp qc

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D. Surface water evaporation

The water evaporation rate from the pond can be determined by Eq. (16) after Smith and
Jones31

_ w ðC1 þ C2 vw Þðpw  pa Þ
m
¼ ; (16)
A DHv

where m _ w =A is the evaporation rate per unit of area, vw is the wind velocity over water sur-
face, pw is the saturation vapor pressure at the water temperature, pa is the saturation vapor
pressure at the air dew point, DHv is the latent heat of water at the pond surface temperature,
and C1 and C2 are constants.
The equation has to be re-arranged in order to use the saturation pressure as a function of
the relative humidity, RH, as shown in Eq. (17)

_ w ðC1 þ C2 vw Þpw ð1  RH=100Þ

m
¼ ; (17)
A DHv

where the values of RH and vw are obtained from annual weather data measured at the site of
interest that were available to the authors.

E. Efficiency
The thermal efficiency of a solar pond can be described as the amount of useful energy
collected, Euc, over a given period of time, divided by the total amount of insolation striking
the pond’s surface, It, as shown in Eq. (18)

Euc
gth ¼ : (18)
It

The useful collected energy can be calculated with the aid of the relation employed by Reza-
chek32 as shown in Eq. (19)

Euc ¼ cbrine Aðz  zLCZ ÞðTsz;f  Tsz;i Þ þ Qrem ðtf  ti Þ; (19)

where cbrine is the heat capacity of the storage zone, A is the effective cross-sectional area of
the storage zone, Tsz,f is the final temperature of the storage zone at time tf, Tsz,i is the initial
temperature of the storage zone at time ti, and Qrem is useful heat removal. The insolation nec-
essary for quantifying Eq. (18) can be determined by integration (Eq. (20))
ð tf
It ¼ I dt: (20)
ti

IV. NUMERICAL APPROACH

A. Preliminary aspects
A set of Navier-Stokes balance equations for a 3 dimensional space was derived using con-
servation of momentum, energy, and mass (salinity). The reason for using three dimensions is
the necessity of describing phenomena like convective vortices, which occur naturally in a fluid
when the density of a lower layer is higher than the one above it. These convective motions
lead to relatively fast transport of mass ensuring the salinity and temperature to be distributed
homogenously throughout the fluid. However, in solar ponds, inside the non-convective zone in
particular, the convective motions are eliminated (ui ¼ 0) due to the density increasing with
depth. Thus, the 3 dimensional analysis is no longer necessary. The transport of thermal energy

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and salinity is then limited to diffusive motions, which occur over longer period of time. There-
fore, Eqs. (10) and (11) are reduced to Eqs. (21) and (22)
 
@T @ @T dIR
qc ¼ K þ ; (21)
@t @z @z dz
 
@S @ @S
¼ D : (22)
@t @z @z

Equations (21) and (22) can now be solved to predict the temperature and salinity profile in the
NCZ and its evolution in time.
In the upper and lower convection zones, where salinity is constant with respect to depth,
thermal convective motions occur, which tend to homogenize salinity and temperature through-
out the layers. It was assumed that these layers act as storage for salt and thermal energy and
interact with the non-convective zone by means of thermal and salt diffusion.

B. Numerical solution
To solve the right hand side of Eqs. (21) and (22) (space derivatives), the finite differences
method was chosen due to its simplicity of implementation, particularly in cases where the
space grid and its boundaries have no complex geometry as is the case of a solar pond. The
space derivative corresponds to the second order central difference. The NCZ has been discre-
tized into N points as shown in Fig. 2, therefore, temperature and salinity information is only
available for these nodes.
With this discretization, the equations of heat conduction and salt concentration flux can be
expressed, respectively, by Eqs. (23) and (24)
" ! #
@Tk 1 X X
0
¼ Djk Kj Dij Ti þ I k ; (23)
@t q k ck j i
!
@Sk X X
¼ Djk Dj Dij Si ; (24)
@t j i

where Dij is the central derivative matrix and k is the number of node. Neumann boundary con-
ditions are considered at the top and bottom surfaces of each zone. The boundary conditions
control the in and out flow from the lower and upper convection zones and both zones are
assumed to constantly be in motion due to convection, therefore mass or heat fluxes get

FIG. 2. Discretization of the NCZ for the finite difference method.

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 053115-9 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

homogenously distributed in the layer in a short period of time. The UCZ and LCZ act as a
storage whose capacity instantly changes as the influx changes. In order to determine the flows
of thermal energy and salt between boundaries, Fourier’s Law (Eq. (26)) and Fick’s law
(Eq. (27)) are used, respectively. With TLCZ and SLCZ being temperature and salinity of the
lower convection zone, respectively, the boundary conditions are expressed by

TN  TLCZ
Q_ R ¼ KNþ12 ; (25)
Dz
SN  SLCZ
JR ¼ DNþ12 : (26)
Dz

For the left hand side of Eqs. (21) and (22) (time derivatives), an explicit 4th order Runge
Kutta method has been chosen and solved for each node of the discretized NCZ. The solution
of both time derivatives is coupled due to their dependency on density, diffusivity, conductivity,
and heat capacity, which further depends on temperature and salt concentration.
Stability of the non-convective zone is examined by numerically calculating a stability indi-
cator, FS, after Eq. (27)

1 @q
FS ¼ ; (27)
q @z

so that the condition of no convective fluid motion is ensured for FS < 0, where z is a depth
coordinate measured from the bottom to the top.

C. Model validation
The model has been validated with literature data of an experimental 232 m2 solar pond
studied in 1982 at the Los Alamos National Laboratory in New Mexico (latitude 36 ) for the
purpose of determining pond’s hydrodynamics with the aid of an underwater pyranometer.28
The pond was constructed from a soft volcanic rock known as tuff (which forms a large frac-
tion of the Los Alamos area surface geology) and was characterized by the ground thermal con-
ductivity of K ¼ 0:05 W=m C, the LCZ thickness of 1.2 m, NCZ of 1.2 m, UCZ of 0.1 m, and
salinity of 22%. The initial temperature of bulk and make-up water was measured to be about
25  C. Weather conditions registry at Los Alamos for the year 1982 were not available28 and
therefore the validation had to be carried out with weather data corresponding with the year
2000.
The starting date for the simulation was set to August 4th, because this coincides with the
first day after the gradient zones had been formed. The data on temperature evolution in the
lower convective zone were provided until October 17th. The solar radiation reduction was
assumed to be 0.8, which is consistent with the measurements carried out in solar ponds of sim-
ilar characteristics.18 With these considerations, the comparison of experimental literature
results with those obtained by our model is shown in Fig. 3.
In addition to validation of LCZ temperatures, calculated and experimental temperature
profiles throughout the different layers were also compared (Fig. 4). Here, a small discrepancy
close to the pond’s surface is found and explained by the fact that numerical results are consid-
ered for the noon, while the factual time of measurement is unknown. It can also be noted that
the divergences between the temperatures registered at the UCZ (at almost ambient tempera-
ture) and those generated with the model can be attributed to the weather conditions in 1982
when the measures were taken, and those of the year 2000, which are the climate conditions
used in the simulation.
The discrepancy between the temperatures registered at the UCZ (at almost ambient tem-
perature), and those generated with the model (Fig. 4) is attributed to the difference in weather
conditions of 1982 when the measures were taken, and those of the year 2000, which the cli-
mate conditions used in the simulation.

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FIG. 3. Validation of the model with experimental data retreived from Jones et al.:28 temperature of lower convective zone
for the period from August 4th till October 17th, 1982.

V. SIMULATION
In order to obtain reliable results from the numerical model, appropriate weather conditions
have to be simulated. For our simulation, the daily average data for temperature, humidity,
wind speed, and insolation had been recorded for 2009 (courtesy of JHG Ingenierıa Ltda.). It
has been assumed that the 2009 data repeat in a yearly period, and therefore a Fourier analysis
was used to obtain continuous data for extended simulation. In order to obtain the performance

FIG. 4. Validation of the model with experimental data retreived from Jones et al.:28 variation of temperature with depth as
of September 3rd, 1982.

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FIG. 5. Change in energy produced in 5 years due to change in NCZ thickness.

of the solar pond in steady state, the simulation was run for 5 years with time step of Dt ¼ 1 h.
In the simulation, the thickness of the UCZ and LCZ has been arbitrary set within the usual
range of values (0.2 m and 0.8 m, respectively)7 while the thickness of the NCZ has been cho-
sen to be of 1.7 m as it maximizes the energy that can be stored in the solar pond (Fig. 5).
Table I summarizes the main parameters used for the simulation.
Two additional assumptions were made. First, in order to allow enough time for the layers
to form and also to heat up the lower convective zone, water is pumped through the heat
exchanger system 2 months after the beginning of operation. Second, all the necessary mainte-
nance requirements are assumed to be met, especially that the salinity gradient in the non-
convective zone is preserved and stable during the operation.

VI. RESULTS AND DISCUSSION

The effective area of the solar pond necessary to meet the energy requirements has been
determined to be of 1431 km2, which would be able to provide 626 439 MWh per year, slightly
exceeding the requirement. A prospective placement of the pond technology next to a mining
operation is shown in Fig. 6.

TABLE I. Parameters for the simulation.

Time Total time 5 years

Time step 1h
Layers UCZ thickness 0.2 m
NCZ thickness 1.7 m
LCZ thickness 0.8 m
Heat exchanger Number of tubes 50
Tube length 200 m
Tube diameter 0.1 m
Fluid velocity 0.1 m/s

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 053115-12 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

FIG. 6. Prospective set of solar pond modules localized next to a leaching pile at the mining operation site in Northern
Chile.

The results here presented were obtained from simulation of pond’s performance for 3
years, in order to ensure that the system has reached steady state. The operation was assumed
to start on January 16th (summer) with heat extraction beginning on March 16th, with the ini-
tial temperature of average ambient (18  C). The initial salinities were 0% for the UCZ and
25.4% for the LCZ.
Figure 7 shows temperature profiles with respect of the depth in the solar pond for the hot-
test and the coldest day of the year.
Figure 8 shows temperature of the LCZ as well as the temperature of the water pumped
from the heat exchanger. Figure 9 shows evolution of pond’s efficiency in the third year of
operation, and Fig. 10 shows the evolution of water evaporation over a year.
From the results, it can be noted that the required surface area is much larger than any so-
lar pond constructed up to date. To facilitate the construction, operation, and maintenance, a
modular configuration is proposed as signalized in Fig. 6. Assuming the cost of water of USD
2 per m3, excavation charges of USD 4.4 per m3, lining cost of USD 6.7 per m2, and the cost

FIG. 7. Temperature profiles in the solar pond for extreme weather conditions (hottest and coldest day).

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 053115-13 Garrido et al. J. Renewable Sustainable Energy 4, 053115 (2012)

FIG. 8. Temperature evolution in LCZ and water extracted from the heat exchanger.

FIG. 9. Evolution of pond’s efficiency during the third year of operation.

FIG. 10. Daily water evaporation in the steady state operation.

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TABLE II. Comparison between constructed and proposed solar pond.

Solar Pond Proposed Beith Ha’Arava26 Pyramid Hill12

Use Process heat Electric energy Process heat

Surface area 1.413 km2 250 000 m2 3000 m2
Load 71.5 MWta 5 MWe 60 kWt
Status N.A. Shut down since 1988 Operative
Cost 240 million USD 20 million USDb (1979) N.A.

a
Average, for an annual thermal energy production of 626 439 MWh.
b
Allocated for R&D, construction of pond and power plant.

of salt of USD 102 per ton, a preliminary estimation suggests an investment of about 240 mil-
lion USD. Comparison of the main characteristics of the proposed pond with two of the exist-
ing ones is shown in Table II.
The results in Fig. 8 indicate that the heat input is delivered within the requested range of
temperatures through the entire year, with the variation of approximately 20  C. The minimum
temperature in the LCZ is that of 47.3  C in winter while the maximum slightly exceeds
64.4  C in summer. Also, it can be seen that the temperature difference between the LCZ and
the pumped flow through the heat exchanger is lower by at least 4.2  C (in winter) and 7.2  C
at most (in summer).
Even though the temperature evolution at the LCZ may suggest a steady state (Fig. 8), effi-
ciency of the solar pond during by the year 3 is still slightly increasing (þ0.2% with respect of
the previous year) as shown in Fig. 9. Nonetheless, it can be stated that the efficiency of the
system is around 19.3% with a variation of 0.1% between summer and winter.
The total evaporated water per year (Fig. 10) amounts to 7 382 210 t (5.16 t/m2) with the
peak of water loss around of 25 000 t per day, occurring in summer and the annual average salt
diffused to the upper layers amounts to 3.28 kg/m2, resulting in a total of 4700 t/year of salt
that has to be reinserted in the LCZ to stabilize the gradient of salinity.
Our simulation assumed that a system of sufficient capacity for daily water replenishment
is available, and therefore water loss does not represent a threat for the stability of the salt gra-
dient. The loss of water due to wind can be reduced using wind suppressors that decrease the
speed of wind over the surface of solar pond, and therefore the spray and wave formation are
reduced. Also, covering the solar pond during the night, when the temperature difference
between the surface and the ambient increases, can reduce the loss of water.
The required stabilization of the salinity gradient can be achieved in one of two ways. The
first is to simply remove the high salinity surface brine and replace it with fresh water, while
new concentrated brine is added to the bottom convective zone. This approach can be realized
in areas where salt is abundant and where salty water can be discarded without posing serious
environmental problems. However, when the pond is located in an area where salt and fresh-
water are relatively costly (which is the case of the Atacama Desert), it is more practical, as
well as economical, to recycle the salt from the brine of the upper convective zone by concen-
trating it and pumping into the lower convective zone.33

VII. SUMMARY AND CONCLUSION

The suitability of solar pond technology to provide the heat necessary for a large-scale
processing of copper ore (leaching) in a mining operation located at the Atacama Desert in
Chile has been studied conceptually. The performance of the solar pond was examined making
use of analytical models and simulated for round year weather conditions with the objective of
ensuring stable energy supply in the required temperature range at all times. The model consid-
ered heat and salt diffusion as well as heat extraction using a set of pipes located at the bottom
of the solar pond. We assumed that the designed solar pond conditions are maintained continu-
ously by addition of make-up water on pond’s top and salt replenishment at the bottom. The

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necessary amount of make-up water and salt were also determined in the study because they
represent critical inputs for the commercial operation of a solar pond. The model was validated
against operational data of the Los Alamos solar pond rendering a close correlation between
the measured and simulation-generated data.
The results of the study indicate that solar pond technology can effectively generate and
store heat to provide temperatures in the range of 50 and 70  C during the whole year, summing
up to the total of 626 439 MWh per year. An effective area of 1.43 km2 would be sufficient to
ensure the supply with an average thermal efficiency of around 19.3% and an estimated
investment cost of 240 million USD. The large land requirements (about 6 times of the Beith
Ha’Arava solar pond) may represent a drawback for the technology as compared with other
alternatives. In order to facilitate the construction, operation, and maintenance of the pond, a
modular configuration is proposed. The annual requirement of make-up water and salt amounts
to 5.17 t/m2 and 3.3 kg/m2, respectively. Due to the scarcity of water and salt resources at the
site, a closed cycle solar pond is suggested, where the diffused salt would be recycled in an
additional evaporation pond.
In comparative terms, to generate the same heat output, a conventional fired heater would
require approximately 59 000 tons of diesel oil per year, with an emission of 164 000 tons of
CO2, among other gases.
Further activities referred to this work should consider the construction of a pilot solar
pond at the site, which would allow its study under weather conditions for a broader time scale
and refine the results here presented.

ACKNOWLEDGMENTS
The authors would like to thank BHP Billiton and JHG Ingenierıa for supporting the develop-
ment of this investigation. We also would like to thank Global Engineering Teams (GET) and Dr.
Marco Eisenberg from TU Berlin for making this project possible under an international
environment.

NOMENCLATURE
A total surface area of the pond (m2)
Ae effective radiation area (m2)
As heat exchanger area (m2)
Ash shaded area (m2)
C constant
c specific heat capacity (J kg1 K)
D coefficient of diffusion (m2 s1)
Euc useful energy collected (W h)
FS stability indicator
g external acceleration (ms2)
Hv latent heat of water (kJ kg1)
h heat transfer coefficient (W m2  C)
I direct radiation flux (W)
I0 incident solar radiation (W)
IR total solar radiation (W)
It integrated insolation (W h)
K coefficient of heat conduction (W m1  C)
L length of a pipe (m)
m_ mass flow rate (kg s1)
MPE mean percentage error (%)
N number of pipes
p pressure, perimeter (kPa), (m)
Q_ rate of heat transfer (kW)
QI energy absorbed in the pond (kJ)

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Qrem useful heat removal (kJ)

R reflectivity
RH relativity humidity (%)
RMSD root mean square deviation
R2 coefficient of determination
S salinity (%)
s salt per time unit (g s1)
Sp surface of the pipe (m2)
S/ external source of /
t time (s)
T temperature (  C)
u velocity (ms1)
vw wind velocity (ms1)
W velocity of the water (ms1)
x horizontal coordinate (m)
z vertical coordinate (m)
a thermal expansion coefficient (K1)
b salinity expansion coefficient
c non convective flow
g constant for wavelength spectra
gth thermal efficiency
h0 coefficient of reduction of solar radiation
#i incident angle
#r refraction angle
l constant for wavelength spectra, fluid viscosity (kg m1 s1)
n fraction of the direct radiation that change to diffuse
q density (kg m3)
r stress tensor
/ arbitrary physical quantity

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