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Energy 41 (2012) 121e127
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Energy
journal homepage: www.elsevier.com/locate/energy
The thermodynamic properties of the upper continental crust: Exergy,
Gibbs free energy and enthalpy
Alicia Valero a, *, Antonio Valero a, Philippe Vieillard b
a
b
CIRCE, Centre of Research for Energy Resources and Consumption, Mariano Esquillor n. 15, 50018 Zaragoza, Spain
CNRS-UMR 6269, 40 Ave du recteur Pineau, 86022 Poitiers cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 2 October 2010
Received in revised form
27 May 2011
Accepted 4 June 2011
Available online 5 August 2011
This paper shows a comprehensive database of the thermodynamic properties of the most abundant
minerals of the upper continental crust. For those substances whose thermodynamic properties are not
listed in the literature, their enthalpy and Gibbs free energy are calculated with 11 different estimation
methods described in this study, with associated errors of up to 10% with respect to values published in
the literature. Thanks to this procedure we have been able to make a first estimation of the enthalpy,
Gibbs free energy and exergy of the bulk upper continental crust and of each of the nearly 300 most
abundant minerals contained in it. Finally, the chemical exergy of the continental crust is compared to
the exergy of the concentrated mineral resources. The numbers obtained indicate the huge chemical
exergy wealth of the crust: 6 106 Gtoe. However, this study shows that approximately only 0.01% of
that amount can be effectively used by man.
Ó 2011 Elsevier Ltd. All rights reserved.
Keywords:
Exergy
Enthalpy
Gibbs free energy
Continental crust
Minerals
Reference environment
1. Introduction
Mankind is facing the fact that some materials are being irreversibly dispersed very rapidly. Phosphates, lithium, coltan
(NbeTa), platinum group metals (PGMs), etc. are some examples
that deserve in-depth studies. It is time to provide objective
guidelines for assessing scarcity. For that purpose, we must develop
tools to move questions from a world of opinions to a world of
quantitative assessments.
The Earth’s continental crust is the accessible reservoir of all the
minerals useful for mankind. The composition and concentration
(ore grade) of a mineral with respect to the bare rock is what
characterizes a resource. If we want to determine what the physical
scarcity is, we need to establish a zero baseline of the available
minerals in the crust. The second law of thermodynamics and
particularly the property exergy plays a fundamental role in this
endeavor. But as is well known, the calculation of the chemical
exergy of any substance from a given reference environment
requires knowing its Gibbs free energy value (Eq. (19)). Furthermore, as stated in [1], a lot of effort has been placed in determining
the chemical composition of the upper continental crust (in terms
of element percentage), but the mineralogical composition of it has
* Corresponding author. Tel.: þ34 976 76 18 63; fax: þ34 976 73 20 78.
E-mail address: [email protected] (A. Valero).
0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.energy.2011.06.012
been barely studied. This is due mainly to the complexity and
heterogeneity of the Earth’s crust.
Hence, we need to tackle two difficulties. The first one is that the
composition of the upper continental crust in terms of minerals is
not known. The second is that current available thermodynamic
data bases about solid substances do not provide empirical information of enthalpies and Gibbs free energies for many of the
minerals appearing in the crust. The first problem was solved
through the proposal of a model of dispersed continental crust
published in [1]. The objective of this paper is thus to solve this
second problem. For that purpose, a selection of the 11 most suitable procedures for calculating thermodynamic properties for the
minerals in the Earth’s crust is carried out. Additionally, different
guidelines are provided for selecting one or other calculation
procedure for each of the substances analyzed with their estimated
associated errors. Furthermore, as an additional output, the
procedure will allow us to obtain the chemical exergy of the Earth’s
upper crust and to compare it with that of the concentrated
minerals, i.e., with what we call mineral resources.
2. Prediction of enthalpy and Gibbs free energy of formation
of minerals
The determination of the thermodynamic properties of the
substances requires knowledge of their corresponding enthalpies
122
A. Valero et al. / Energy 41 (2012) 121e127
DH0f and Gibbs free energies of formation DG0f . Many of these have
been already estimated through empirical and semi-empirical
processes1 and are tabulated. Comprehensive compilations of the
thermodynamic properties of inorganic substances can be found in
Faure [2], Wagman [3], Robie et al. [4,5], or Weast et al. [6].
Unfortunately, not all the enthalpies and Gibbs free energies of
the minerals that compose the Earth’s upper crust are recorded in
the literature.
If either DH0f or DG0f and the entropy (s0) of the mineral under
consideration are available, the unknown property can be easily
calculated from the fundamental relationship derived from the
combined first and second laws of thermodynamics (Eq. (1)).
DG0f ¼ DH0f T0 $DS
(1)
The entropy change DS is calculated from the standard entropy
of the mineral and its constituent elements in the standard state
(T0 ¼ 298.15 K and 1 bar), as in Eq. (2):
DS ¼ s0mineral X
ni s0elements
(2)
Note that this procedure does not have any associated error,
since it is based on standard entropies of elements in the reference
state.
The thermodynamic properties of many substances can be also
predicted satisfactorily through different semi-empirical methods.
Developed with different assumptions, these can be grouped into
four main classes: a)- methods based on theoretical models in
which minerals are considered a solid solution of two or more endmembers; b)- statistical methods which describe the thermodynamic function as a linear combination of crystallochemical variable as the stoichiometry; c)- parametric methods to assign one or
more parameters to each element or compound ion and d)- specific
methods not included in any of the previous classes.
2.1. Group A: The solid solution model
Consider a solid solution in which one and only one ion
substitutes for another. The enthalpy and entropy produced in such
ideal mixing (m) are:
DHm ¼ 0
DSm ¼ ni $R$
(3)
X
xi ,lnxi
(4)
In which ni is the total number of sites (per formula unit) on
which mixing takes place, and xi is the mole fraction of the i-th ion
in the site. This means that for enthalpy, the ideal mixing will take
place without any heat loss or heat production. And for entropy,
a random mixing of cations on the same crystallographic site will
take place [7]. The enthalpy and Gibbs free energy of formation of
the solid solution are obtained as follows:
DH0f ; solution ¼
X
xi DH0f ;i
(5)
i
DG0f ; solution ¼
X
i
xi DG0f ;i þ ni RT
X
xi lnxi
(6)
The error associated to the assumption of the mineral as an ideal
solid solution varies greatly with the mineral under consideration
and decreases with the disorder among components. We will
assume a maximum error of 1%.
1
Such as calorimetric or solubility measurements.
2.2. Group B: Statistical methods
Models presented in this section are the statistical results of
computation from an internal set of consistent data. Two models
have been chosen and addressed for silicates and hydrates.
2.2.1. The method of Chermak and Rimstidt for silicate minerals
The method proposed by Chermak and Rimstidt [8] predicts the
thermodynamic properties (DG0f and DH0f ) of silicate minerals from
the sum of polyhedral oxide and hydroxide contributions. The
technique is based on the observation that silicate minerals have
been shown to act as a combination of basic polyhedral units.
Chermak and Rimstidt [8] determined by multiple linear regres½4
½6
½6
½4
sion, the contribution of Al2 O3 , Al2 O3 , AlðOHÞ3 , SiO2 , MgO½6 ,
½6
MgðOHÞ2 , CaO½6 , CaO½8z , Na2 O½68 , K2 O½812 , H2 O, FeO½6 ,
½6
FeðOHÞ2
½6
and Fe2 O3 to the total DG0f and DH0f of a selected group of
silicate minerals.2 The thermodynamic properties of the minerals
are calculated with Eqs. (7) and (8).
DH0f ¼
DG0f ¼
X
X
xi $hi
(7)
xi $gi
(8)
Where xi is the number of moles of the oxide or hydroxide per
formula unit and hi and gi are the respective molar enthalpy and
free energy contribution of 1 mol of each oxide or hydroxide
component. The values of hi and gi for the different polyhedral
components are listed in [8].
The errors associated to the estimated versus experimentally
measured values can reach 1% for DG0f and DH0f , depending on the
nature of the compounds. Note that this methodology can only be
applied to those minerals able to be decomposed by the oxides and
hydroxides mentioned before. For other elements bearing silicates,
there is no way to predict their thermodynamic properties with this
prediction model.
2.2.2. Model of prediction of DH 0f and DG0f for hydrates
Hydrated minerals have the ability to absorb water molecules,
forming part of their crystal structure:
A þ n$H2 O/A$nH2 O
Usually, thermodynamic properties are available for the nonhydrated mineral. But the enthalpy and Gibbs free energy of
formation of the hydrated substance can be estimated by addition
of the hydration enthalpy DH0hydr and Gibbs free energy DG0hydr to
those of the dehydrated substance, as in Eq. (9).
DH0f ;A,nH2 O ¼ DH0f ;A þ n$DH0f H2 O þ DH0hydr;A
DG0f ;A,nH2 O ¼ DG0f ;A þ n$DG0f H2 O þ DG0hydr;A
(9)
If DG0hydr and DH0hydr of a hydrated compound A$nH2O are not
available, one can assume that the enthalpy and Gibbs free energy
of the hydration reaction are null (as in section 2.4.3). Hence, the
properties of the liquid water molecules contained in the hydrated
substance must be added (Eq. (9)). This is not rigourously exact, as
demonstrated by Vieillard and Jenkins ([9e11]) and the error
associated depends on the nature of the dehydrated component.3
2
The brackets next to the chemical formulas of oxides and hydroxides indicate
the coordination number of the polyhedral structure.
3
This methodology is not applied for hydrated clay minerals and phyllosilicates.
In those cases, the DO2method is applied.
A. Valero et al. / Energy 41 (2012) 121e127
We will assume an associated error of 5%, although it rarely
exceeds 2%.
2.3. Group C: Parametric methods
Methods tested on different mineralogical families are based on
the electronegativity difference defined by Pauling [12] in which
the electronegativity is the power of an atom in a molecule to
attract electrons to another atom. The greater the difference of the
electronegativity between atoms A and B, the stronger will be the
energy of formation of the compound.
2.3.1. The DO2 method
The Pauling’s concept has been extensively developed by Yves
Tardy and colleagues [13e17] by defining the parameter DO2.
The parameter DO2, corresponds to the enthalpy DHO2 or
Gibbs free energy4 DGO2 of formation of a generic oxide MOx(c)
from its aqueous ion, where z is the charge of the ion and x the
number of oxygen atoms combined with one atom M in the
oxide (x ¼ z/2):
DH O2 Mzþ ¼
i
1h 0
zþ
DHf MOxðcÞ DH0f MðaqÞ
x
(10)
For hydroxides [9], silicates [10,12], phosphates [13], nitrates
and carbonates [17] involving two cations, it was found that the
enthalpy and Gibbs free energy of formation of a given compound
from its constituent oxides vary linearly with DO2 and have the
general expression:
DH0ox ¼ aH
ni $xi $nj $xj
zþ
zþ
DH O2 Mi i ðaqÞ DH O2 Mj j ðaqÞ
N
(11)
Being DH0ox 5:
h
i
h
i
DH0ox ðMi Þni Mj n ON ¼ DH0f ðMi Þni Mj n ON ni DH0f Mi Oxi ðcÞ
j
j
nj DH0f Mj Oxj ðcÞ
(12)
Where ni and nj are the numbers of oxygen ions linked, respectively,
zþ
to the molecular structure of the double oxide (N ¼ ni$xi þ nj$xj) and Xi
and Xj are the molar fractions of oxygen atoms respectively related to
cations
zþ
Mi i
and
zþ
Mj j
in the individual oxides MiOxi and MjOxj.
Parameters aH and aG are empirical coefficients variable from one
family of compounds to another one. The enthalpy of formation of
minerals as derived from their constituent oxides appears to be
proportional to three parameters: (1) coefficient aH which relates to
the nature of the family, (2) the stoichiometric coefficient ni$xi$(nj$xj)/
zþ
zþ
N, and (3) the difference DH O2 Mi i ðaqÞ DH O2 Mj j ðaqÞ.
We will assume a maximum error associated to the DO2
general method of 1%.
2.3.2. The DO2 method for different compounds with the same
cations
Tardy [18] showed that the Gibbs free energy of formation of
a compound from its two constituent oxides calculated per one
oxygen atom in the formula was a parabolic function of mean DO2
compound. Subsequently, an expression for calculating the Gibbs
free energy of formation of a compound C intermediate in
composition to two compounds A and B, A þ B / C was developed:
4
5
zþ
zþ
DGox;AþB/C ¼ a,nC DG O2 Mi i DG O2 Mj j , XiC XiA
XiC XiB
The calculation of DGO is analogous to that of DHO
The calculation of DG0ox is analogous to that of DH0ox .
2
2
.
(13)
where nc designates the total number of oxygen ions of the
compound
and XiA ;XiB ;XiC , the mole fractions of oxygen that balance
zþ
cation Mi i in compounds A, B, and a the correlation parameter for
a given class of compounds.
2.3.3. Extension of the DO2 method for different crystallochemical
families of minerals
A generalization of the model of prediction of enthalpies of
formation (aH ¼ 1) has been done by considering two different
energetic states of a cation Mzþ in a free oxide supported as a reference
and in an oxide involved in a complex mineral [19,20]. So, the enthalpy
of formation of a mineral from constituent oxides, is considered as the
sum of the products of the molar fraction of an oxygen atom bound to
any two cations multiplied by the electronegativity difference defined
by the DGO2Mzþ (comp) between any two consecutive cations
[21,22]. Vieillard applied the formalism described above for the
prediction of thermodynamic properties of formation for hydrated
clay minerals [23], for phyllosilicates (24), for alunite minerals [25], for
zeolites [26] and for sulphides [27]. Next, the methods for obtaining
the properties of hydrated clay minerals, phyllosilicates and sulfosalts
is shown.
2.3.3.1. Hydrated clay minerals and Phyllosilicates. The Gibbs free
energy of formation of a hydrated clay mineral or a phyllosilicate
composed by ns cations located in different crystal sites and with ns
(ns1)/2 interaction terms is calculated as:
DG0f ¼
iX
¼ ns
i¼1
ðni ÞDG0f Mi Oxi ðcÞ þ DG0ox
(14)
The Gibbs free energy of formation from the oxides DG0ox is
calculated with Eq. (15):
zþ
to the Mi i and Mj j cations; and N is the number of oxygen ions linked
123
DG0ox ¼ N$
¼ ns
i ¼X
ns 1 jX
i¼1
DG O
2
j ¼ iþ1
Xi Xj $ DG O2 Mizi þ ðclayÞ
zþ
Mj j ðclayÞ
(15)
where N is the total number of O atoms of all oxides; Xi and Xj are
zþ
the molar fraction of oxygen related to the cations Mizi þ and Mj j in
the individual oxides MiOxi and MjOxj, respectively Xi ¼ (1/N)(nixi)
and Xj ¼ (1/N)(njxj). The Gibbs free energy of formation from
constituent oxides is considered as the sum of the products of the
molar fraction of an oxygen atom bound to any two cations
multiplied by the electronegativity difference defined by the
DGO2Mzþ (clay) between any two consecutive cations. The
DGO2Mzþ (clay) value listed in [23,24], using a weighting scheme
involving the electronegativity of a cation in a specific site (interlayer, octahedral and tetrahedral) is assumed to be constant and
can be calculated by minimization of the difference between
experimental Gibbs free energies (determined from solubility
measurements) and calculated Gibbs free energies of formation
from constituent oxides. The predicted Gibbs free energy values
showed an error between 0.0 and 0.6%.
2.3.3.2. Sulfosalts. Craig and Barton [28] developed an approximation method for estimating the thermodynamic properties of
sulfosalts in terms of mixtures of the simple sulfides. The ideal
124
A. Valero et al. / Energy 41 (2012) 121e127
mixing model does not apply correctly to most sulfosalts, because
the mixtures of layers are rather ordered. The modified ideal mixing model of Craig and Barton involves a mixing term (DGm) in the
estimation of the Gibbs free energy of formation of the sulfosalt per
gram atom of S that is added to the weighted sum of free energies of
the simple sulfides:
DGm ¼ ð1:2 0:8Þ$ RT
X
xi lnxi
(16)
The mixing term can be divided into two parts, one estimated
from the crystal structure as an entropy change, and the reminder
as a non-ideal term. The non-ideal term of this model was assumed
to be constant for all sulfosalts. However, Vieillard [27] showed that
the properties of complex sulfides with respect to their simple
sulfides are a function of the electronegativity difference between
the cations of the sulfosalt.
The thermodynamic properties of sulfosalts (sfs) may then be
calculated by adding a term (DHsulf or DGsulf) to the appropriately
weighted sum of the enthalpies or free energies of the simple
component sulfides:
DHf ;sfs ¼
DGf ;sfs ¼
X
X
xi DHf ; sulfides þ nS;sfs DHsulf
(17)
xi DGf ;sulfides þ nS;sfs DGsulf
(18)
The reaction term, which is analogous to the mixing term of
Craig and Barton is associated to one atom of sulfur in the mineral
(nS,sfs) and is obtained from a sulfosalt for which its thermodynamic
properties and those of its simple sulfides are known. The calculated reaction terms can be applied to a family of sulfosalts formed
by the same cations and with partial element substitutions.
Vieillard et al. [27] demonstrated the analogy between the electronegativity scale of cations with respect to sulfur and to oxygen.
They showed that the methodology of estimation of the thermodynamic properties of double-oxides from simple oxides can be equally
applied to sulfosalts able to be decomposed into simple sulfides. As
for double-oxides, the reaction terms DHox and DGox (for this case
denoted as DHsulf and DGsulf) should be obtained for a sulfide of the
same family of the mineral under analysis. The maximum error
associated to this methodology is assumed to be 1%.
the reaction involved in the formation of the mineral is zero. This
procedure named Helgeson’s algorithm, is useful when either DGf
or DHf are known. Once the entropy of the mineral is known, DGf (or
DHf) can be calculated with DHf (or DGf) through Eq. (1). The error
associated to this approximation is up to 5%.
2.4.3. Cases for which thermodynamic data are scarce or absent for
some minerals belonging to a same crystallographical family e
Assuming DHr or DGr zero e the element substitution method
In this case, the DH0f and DG0f of mineral B can be calculated from
mineral A, assuming that the reaction enthalpy or free energy of
formation of mineral B from A is zero. This approximation increases
with the magnitude of substitution and may yield to associated
errors of up to 5%, although it rarely exceeds 2%.
2.4.4. Cases for which thermodynamic data are scarce or absent for
some minerals belonging to a same crystallographical family e
Assuming DHr or DGr zero e the splitting method
If none of the previously described methods can be applied, the
thermodynamic properties of a certain mineral can be estimated in
the last resort by splitting it into its major constituents for which
the enthalpy and Gibbs free energy of formation are known. It will
be assumed that the energy of reaction of the constituents to form
the mineral under consideration is zero. The error associated to this
methodology is significantly greater than with the substitution and
addition methods, since in this case we are not dealing with partial
substitutions or additions of a known mineral, but with the
formation of a completely new mineral from its building blocks.
The mineral under analysis will be broken down into its most
complex compounds (usually double silicates). If this is not
possible, most minerals can be splitted into their simple oxides,
sulfides, carbonates, etc. We will assume that the decomposition
method throws an error of up to 10%.
2.5. Summary of the methodologies
The described methodologies in the previous sections, will be
used for calculating the thermodynamic properties of the most
abundant minerals in the Earth’s upper crust. The assumed
maximum errors associated to the estimation methods (ε) are
given in Table 1.
2.4. Group D: Specific methods
This section lists all the different methods of computation of
thermodynamic properties of some compounds for which thermodynamic properties are available for a certain mineral (A),
belonging to the same family of the substance under consideration
(B), but with partial element substitutions.
2.4.1. Cases for which thermodynamic data are present for some
minerals belonging to a same crystallographical family
For some compounds having a close similarity with minerals for
which DH0f , DG0f or s0 are present, a way to evaluate their thermodynamic properties can be made possible by assuming
a constancy, DHr and DGr for the substitution reaction of minerals
A-x and B-x into A-y and B-y, only if A-x and B-y are isomorphous.
The so called “method of corresponding states” has been developed
by Karapet’yants [29] and the associated error is assumed to be
equal to the previous method, hence 1%.
2.4.2. Cases for which thermodynamic data are scarce or absent for
some minerals belonging to a same crystallographical family e
Assuming DSr zero
Helgeson et al. [30] showed that the entropy of formation of
a certain mineral can be determined assuming that the entropy of
3. Results
Table A1 shows the thermodynamic properties of the 291 main
minerals included in the crust [41e49]. About a half of the
Table 1
Summary of the methodologies used to predict the thermodynamic properties of
minerals.
Method
The solid solution model
The method of Chermak and Rimstidt for
silicate minerals
The addition method for hydrated minerals
The DO2 method
The DO2 method for different compounds
with the same cations
The DO2 method for hydrated clay minerals
and for phyllosilicates
Thermochemical approximations for sulfosalts
and complex oxides
The method of corresponding states
Assuming DSr zero
The element substitution method
The splitting method
Nr.
ε, %
1
2
1
1
3
4
5
5
1
1
6
0.6
7
1
8
9
10
11
1
5
5
10
A. Valero et al. / Energy 41 (2012) 121e127
properties (159) were compiled directly from the literature. The
remaining was obtained using the 11 different estimation methods
described previously. From the latter, the properties of five minerals
were estimated as committing a maximum error of ε<0.6%. Thirtyeight minerals were estimated with an error smaller than 1%, 20
substances with ε<5 %, and 44 minerals with ε<10 %. Only the
properties of 6 minerals: iridium, osmium, nickeline, polixene,
sylvanite and yttrialite were not able to be estimated. Additionally,
the enthalpy of formation of gersdorffite and the Gibbs free energy
of smaltite are missing. Nevertheless, all together account for only
3.5106 % of the continental crust.
With the Gibbs free energy values, we can obtain the chemical
exergy (bchi) of each substance in kJ/mol through Eq. (19):
bchi ¼ DGf þ
X
nj;i bchj
(19)
j
where bchj is the standard chemical exergy of the elements nj,i that
compose substance i. In our case we will use the chemical exergy of
the elements obtained with an update of Szargut’s reference
environment [31] and published in [32].
It should be pointed out that the R.E. generates some negative
exergies of the minerals. This is because we chose our R.E. based on
Szargut’s criterion of partial stability. According to this, among
a group of reasonably abundant substances, the most stable will be
chosen if they also satisfy the “Earth similarity criterion”. This
criterium is different from that of [33] or [34], where complete
stability was assumed. As a consequence, the latter R.E. do not
generate any negative exergies, but the resulting environment is
completely different from that of the current Earth. The chosen R.E.
obeys in principle the “Earth similarity criterion”, but does generate
some negative exergies. Hence, this leads us to question the
methodology used for establishing the R.E.
From this study, a comprehensive database of more than 2000
entries of the enthalpy, Gibbs free energy and exergy of these
minerals composing the crust, together with other important
industrial substances has been developed and included in the
Exergy calculator of the Exergoecology Portal (http://www.
exergoecology.com).
3.1. The chemical exergy of the Earth
Assuming that the upper continental crust is composed of an
ideal solution of substances, its average Enthalpy (DHf ), Gibbs free
energy (DGf ) and chemical exergy (bch ) expressed in kJ/mol of
upper crust, is calculated as:
DHf ¼
m X
xi $DHfi
(20)
i¼1
DGf ¼
m
X
xi $ DGfi þ RT0 lnxi
(21)
i¼1
bch ¼
m
X
xi $ðbchi þ RT0 lnxi Þ
(22)
i¼1
Being xi, molar fraction of the species composing the crust, and
DHfi, DGfi and bchi, their enthalpy, Gibbs free energy and chemical
exergy in kJ/mol, respectively.
The enthalpy and Gibbs free energy of the substances are
obtained either through the literature or through the estimation
methods explained before.
The average enthalpy, Gibbs free energy and exergy of the
continental crust, can be expressed in mol/g by substituting xi with
125
the molar fraction xi for the i constituents of the upper crust. Eq.
(23) relates both properties through the molecular weight of the
upper continental crust which was obtained in [1] as equal to
MWcr ¼ 155.2 g/mol:
xi ¼ xi $MWcr
(23)
Hence, the properties of the upper continental crust calculated
are the following:
0
DHf
¼ 2300:37 kJ=mol
cr
0
DGf
¼ 2162 kJ=mol
0 cr
bch
¼ ¼ 3:63 kJ=mol
cr
For the calculation of the absolute exergy of the continental crust,
we require information about its total mass. According to [35], the
Earth has a mass of around 5.981024 kg. The Earth’s relative mass
proportions of each of its spheres are according to [36]: core (35.5%),
mantle (67%), oceanic crust (0.072%), continental crust (0.36%),
hydrosphere (0.023%) and atmosphere (0.842 ppm). The upper layer
of the crust constitutes a mass of around 50% of the whole continental
crust [37]. With this information we can obtain a first approximation
of the exergy of the upper continental crust (see Table 2). It has been
assumed that there is no mixing among the considered layers and
hence the Gibbs free energy and exergy of mixing is zero.
Accordingly, a first estimation of the exergy of the bulk Earth has
been estimated at around 6106 Gtoe. Obviously this is a very rough
number since it accumulates each of the different sources of errors
mentioned above. Nevertheless, it is good enough, for providing an
order of magnitude of the chemical exergy of our planet.
In [38] we carried out an inventory of the exergy resources of the
Earth. For the case of non-renewable resources, including nuclear
energy, fossil fuels and non-fuel minerals, the estimation of the
available exergy on Earth obtained was at least around 115,000 Gtoe,
from which 65% come from the not yet technologically developed
fusion of deuterium and tritium. The potential exergy use of nonrenewable resources was around 6000 Gtoe, from which near 900
Gtoe came from conventional fossil fuels and minerals. Considering
these figures, we can now state that the non-renewable currently
available resources contribute to a very small fraction of the total
chemical exergy of the Earth: around 0.1%. Furthermore, the exergy of
conventional fossil fuels and non energy mineral resources, constitute only 0.01% of the upper continental crust’s chemical exergy.
The obtained values are subject to different sources of errors.
Firstly, the composition of the crust used and the relative proportion of each of the minerals xi in the crust is based on the crepuscular crust model developed in [1]. The latter model is
a preliminary study based on the work of Grigor’ev [39] and
ensuring coherence between the chemical composition of the crust
in terms of elements (which is reasonably well known thanks to the
contribution of a good number of geochemical studies in the last
century), and the composition in terms of minerals (for which
except of the work of Grigor’ev [39], no significant studies have
been carried out due to the complexity and heterogeneity of the
crust). The model was additionally completed with different
hypotheses based on geological and geochemical observations.
Hence, it is expected that xi will be updated in the future when
better geological and geochemical information is available. The
second source of error can be found in the the assumption of
Table 2
Exergy of the bulk upper crust.
0
0
Mass, kg
MW, g/mol
bch , kJ/mol
Bch , Gtoe
1.08E þ 22
155.2
3.63
6.02E þ 06
126
A. Valero et al. / Energy 41 (2012) 121e127
considering only one chemical composition per mineral. In fact, any
one mineral can have slight variations in composition. For instance,
the general chemical formula of oligoclase is (Na,Ca)(Si,Al)4O8.
Under the latter, many different chemical compositions of oligoclase may appear. In this study we have assumed the empirical
formula, which is derived from the mineral’s structural (molecular)
formula by using the published analysis of the mineral or deriving
the analysis using basic rules [40]. The third source of error is
associated to the different estimation methods explained in this
paper for obtaining the enthalpy and Gibbs free energy of formation
of the minerals. And finally, another source of error for the exergies
obtained, is due to the reference environment used, as explained
previously.
4. Conclusions
In this paper we have provided tools for the thermodynamic
evaluation of any physical substance on Earth. Moreover, the
standard thermodynamic properties of the main constituents of the
upper Earth’s crust have been obtained. That is the standard
enthalpy, Gibbs free energy and chemical exergy of about 300
natural substances.
The enthalpies and Gibbs free energies, have been obtained
either from the literature, or have been calculated using the 11
estimation methods described in this paper. The exergy of the
substances has been calculated with the chemical exergies of the
elements, generated with an R.E. based on Szargut’s methodology.
Despite the limitations of the R.E. pointed out, it still constitutes
a tool for obtaining chemical exergies.
The model of the upper continental crust developed in
a previous study together with the calculation methodologies
presented in this paper have allowed us to calculate additionally
the absolute chemical exergy of this sphere as 6.0106 Gtoe.
Obviously the numbers are very rough, and are subject to further
updates, but they are good enough for providing an order of
magnitude of the huge chemical wealth of our planet.
Unfortunately, man can only take advantage of a very small part
of it: the resources. With current technology and except in very
uncommon cases, it is impossible to use the chemical exergy of
dispersed substances. Non-renewable resources are considered as
such, because they represent a stock of concentrated chemical
exergy. Each time man converts resources into dispersed and
degraded substances, the mineral capital on Earth decreases irreversibly. Therefore, the Earth’s 6.0106 Gtoe of chemical exergy
constitutes nowadays a useless reservoir of exergy and we should
resign ourselves to a maximum of only around 0.01% of that
amount.
Acknowledgments
This study has been carried out under the framework of the
ENE2010-19834 project financed by the Spanish Ministry of
Education and Science.
Appendix. Supplementary material
Supplementary data associated with this article can be found in
the online version, at doi:10.1016/j.energy.2011.06.012.
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