Page 6
Methods:Exergycontentofflows
6
24 CHAPTER 3. EXERGETIC LCA IMPLEMENTATION
at elevated pressures (e.g. natural gas from a production well). For the LCA of
CO2
absorption processes, the pressure-dependent physical exergy of the compressed
CO2
stream is computed separately and treated as a produced material by the MEA
absorption process. It is assumed not to reenter the ecosphere within the boundaries
of this analysis.
3.3.3 Temperature-dependent
Key rows
The temperature-dependent physical exergy for each key row i from process j is
calculated as:
b
phT,i,j
= c
p,i
✓T
i,j
� T
0
� T
0
ln
✓T
i,j
T
0
◆◆ MJ
mol
�, (3.14)
where bphT,i,j
⇥MJ
mol
⇤is the temperature-dependent physical exergy of substance i from
process j, cp,i
⇥MJ
mol K
⇤is the specific heat capacity of substance i at constant pressure,
T
i,j
[K] is the temperature of substance i, and T
0
[K] is the temperature of the reference
environment.
In this study c
p,i
is held constant for all processes j, regardless of temperature Ti,j
,
although in future implementations cp,i
could be computed dynamically as a function
of temperature. As T0
is specified for the all reference environments (T0,air
= T
0,soil
=
T
0,water
= T
0,raw
= 287.05 [K] [35] and T
i,j
is specified for all flows and processes in
Bkey
(see Table 5.4 in Appendix), the above calculation is relatively straightforward
in most cases.
In several cases rows which should be more accurately thought of as mass through-
puts (such as “water, turbine use” and “water, cooling”) are treated only as inputs
within ecoinvent. This contributes to the non-mass conserving nature of the ecoin-
vent v3 database. However these through-puts are assumed to intake mass at en-
vironmental temperature T
0
and then output that mass at an elevated temperature
T
i,j
[46, 47, 48], meaning for the purposes of physical exergy calculation they are
reclassified as outputs in the “water” category.
22 CHAPTER 3. EXERGETIC LCA IMPLEMENTATION
rows and 4 RoE rows.
One additional key input row is added to Bkey
, for the mass flow of produced water
during geothermal electricity generation. This flow is not included in the ecoinvent
database and, like the combustion gases, is manually added to Bkey
afterwards based
on calculations of water and steam production rates and typical geothermal power
plant e�ciencies in the literature [45]. Key processes for this row include only the 13
geothermal electricity production processes in B. The final reduced size of Bkey
is 16
key rows by 261 columns, with 4 RoE rows comprising the remainder of B.
Relevant physical data is collected for all key rows and columns, including temper-
ature of each flow from each process Ti,j
[K] and the specific heat at constant pressure
of each flow c
p,i
⇥MJ
mol K
⇤(see Table 5.4 in Appendix).
3.3.2 Pressure-dependent
The equation for pressure-dependent physical exergy of substance i from process j,
modified from Section 2.2 is:
b
php,i,j
= R T
0
ln
✓p
i,j
p
0
◆ MJ
mol
�, (3.12)
where b
php,i,j
⇥MJ
mol
⇤is the pressure-dependent physical exergy of substance i from
process j, R⇥
MJ
mol K
⇤is the universal gas constant, T
0
[K] is the temperature of the
environment, pi,j
[kPa] is the pressure of the substance, and p
0
[kPa] is the pressure
of the reference atmosphere.
In this study it is assumed that all waste and raw material flows leaving or entering
the technosphere do so at atmospheric pressure. Thus pi,j
= p
0
[kPa] in all cases, and
the pressure-dependent physical exergy for any substance i becomes:
b
php,i
= R T
0
ln
✓p
0
p
0
◆= 0
MJ
mol
�. (3.13)
This assumption is a reasonable one for waste flows, which are generally not released
to the environment at significantly higher than atmospheric pressure. However, it does
neglect the exergy associated with natural resources which may enter the technosphere
3.4. CHEMICAL EXERGY 31
Table 3.6: Assumed RoE values for chemical exergy.
Argon Avg. PCC Avg. NGCC Methane
N.S. chem. ex. [kJ mol�1] 11.690 a N/A N/A 831.640 a
Molar mass [g mol�1] 39.948 N/A N/A 16.040
b
ch,Air
[kJ kg�1] 293 559 616 51,847b
ch,Soil
[kJ kg�1] 293 17,104 16,534 51,847b
ch,Water
[kJ kg�1] 293 4,750 3,847 51,847b
ch,Res.
[kJ kg�1] 293 30,328 46,623 51,847
a - [14, 27]
formula and Gibbs free energy of formation. Three cases are run, representing a ‘best-
case’, ‘middle-case’, and ‘worst-case’ assumption for the chemical exergy intensity of
the RoE rows (see Table 3.6).
3.4.3 Di↵usive exergy loss
Key rows
The general equation for the calculation of di↵usive chemical exergy loss for a partic-
ular row in Gkey
, from Section 2.3 is:
b
mix,i
= R T
0
↵
i
X
j
ln (yi,j
)
MJ
mol
�, (3.20)
where b
mix,i
⇥MJ
mol
⇤is the di↵usive chemical exergy loss, R
⇥MJ
mol K
⇤is the universal gas
constant, T0
[K] is the temperature of the reference environment, ↵i
is the activ-
ity coe�cient of substance i relative to an ideal substance, and y
i,j
hmol i, j
mol j
iis the
concentration of substance i in process j.
Concentration y
i,j
for resource input rows, in the case of ores, is taken from the
ecoinvent database, which specifies the mass percent of the target substance relative
to the total ore. Determining concentrations for output substances on the other
hand is more di�cult, as no data is contained within the ecoinvent database on
concentrations of waste flows. Instead, this study assumes a simplified ‘three-pipe’
28 CHAPTER 3. EXERGETIC LCA IMPLEMENTATION
3.4.2 Normal standard chemical exergy
Key rows
The general method for calculating normal standard chemical exergy of a substance
in the inventory matrix Gkey
given in Section 2.3 is:
b
0
NS,i
= �f
G
0
i
+X
el
n
el
b
0
chel
MJ
mol
�, (3.16)
where b
0
NS,i
⇥MJ
mol
⇤is the normal standard chemical exergy of substance i, �
f
G
0
i
⇥MJ
mol
⇤
is the Gibbs free energy of formation for substance i, nel
is the stoichiometric number
of moles of element el in substance i, and b
0
chel
⇥MJ
mol
⇤is the normal standard chemical
exergy of element el in substance i.
This method is used for the majority of key rows - those which have identifiable
chemical formulae and Gibbs values. However, not every row fits this model, and
several special calculation methods are employed to handle unconventional rows.
For organic fuels which typically do not have established, consistent chemical for-
mulae (as in the case of coal, liquid hydrocarbons, or biomass) the following equation
is used:
b
0
NS,i
= HHVi
r
i
MJ
kg
�, (3.17)
where HHVi
hMJ
kg
iis the higher heating value of the i
th fuel per unit mass, and r
i
is
the ratio of standard chemical exergy of the i
th fuel to its higher heating value, as
given in Table 3.5.
In several cases, special consideration is given to flows which are considered to
be withdrawn from the environment, passed through the human economy, and then
re-emitted without chemical alteration. These are termed ‘unaltered flows’ in this
study, and represent flows such as water taken from a stream and run through a
once-through cooling system, or water flowing through a hydroelectric damn. In
3.5. GRAVITATIONAL POTENTIAL EXERGY 33
a lack of information regarding mixing behaviors of the key rows. This assumption
has the e↵ect of over estimating the total di↵usive chemical exergy loss of a row,
particularly for ionic species in water, and solids, which behave far from ideally.
Rest of economy
Di↵usive chemical exergy loss for all RoE rows are computed using the general
Equation 3.20. However, all RoE rows are assumed to be output or input as pure
substances with a concentration y
i,j
= 1⇥mol
mol
⇤. Therefore the di↵usive exergy loss
b
mix,RoE
= R T
0
↵
i
ln (1) = 0⇥MJ
mol
⇤for all RoE rows. This is a conservative assump-
tion.
3.5 Gravitational potential exergy
The equation for the calculation of the total gravitational potential exergy of an
inventory matrix G is:
B
pe
= g
X
i
X
j
m
i,j
(zi,j
� z
0
) = g
X
i
X
j
m
i,j
�z
i,j
[MJ] , (3.22)
where g
⇥km
s
2
⇤is the gravitational constant, m
i,j
[kg] is the mass of substance i in
process j, zi,j
[km] is the elevation at which the i
th substance from the j
th process is
emitted, and z
0
[km] is the reference elevation of the natural environment. For the
purposes of this study z
0
for all reference environments is chosen to be sea level, or 0
[km].
3.5.1 Reduction of matrix size
As with physical and chemical exergy, gravitational potential exergy exists only for
the rows of B which are in units of mass or volume. Thus, all volumetric flows are
converted to mass and all calculations are performed on the same 920 row Bmass
constructed in Section 3.3.
3.5. GRAVITATIONAL POTENTIAL EXERGY 33
a lack of information regarding mixing behaviors of the key rows. This assumption
has the e↵ect of over estimating the total di↵usive chemical exergy loss of a row,
particularly for ionic species in water, and solids, which behave far from ideally.
Rest of economy
Di↵usive chemical exergy loss for all RoE rows are computed using the general
Equation 3.20. However, all RoE rows are assumed to be output or input as pure
substances with a concentration y
i,j
= 1⇥mol
mol
⇤. Therefore the di↵usive exergy loss
b
mix,RoE
= R T
0
↵
i
ln (1) = 0⇥MJ
mol
⇤for all RoE rows. This is a conservative assump-
tion.
3.5 Gravitational potential exergy
The equation for the calculation of the total gravitational potential exergy of an
inventory matrix G is:
B
pe
= g
X
i
X
j
m
i,j
(zi,j
� z
0
) = g
X
i
X
j
m
i,j
�z
i,j
[MJ] , (3.22)
where g
⇥km
s
2
⇤is the gravitational constant, m
i,j
[kg] is the mass of substance i in
process j, zi,j
[km] is the elevation at which the i
th substance from the j
th process is
emitted, and z
0
[km] is the reference elevation of the natural environment. For the
purposes of this study z
0
for all reference environments is chosen to be sea level, or 0
[km].
3.5.1 Reduction of matrix size
As with physical and chemical exergy, gravitational potential exergy exists only for
the rows of B which are in units of mass or volume. Thus, all volumetric flows are
converted to mass and all calculations are performed on the same 920 row Bmass
constructed in Section 3.3.
34 CHAPTER 3. EXERGETIC LCA IMPLEMENTATION
Elevation data for most rows and processes is absent in the ecoinvent database.
Therefore the output and input elevations zi,j
[km] for most substances in Bmass
are
assumed to be sea level, such that �z
i,j
= 0 [km] and b
pe,i
= 0hMJ
kg
i.
The one exception to this assumption is the row “Water, turbine use, unspecified
natural origin”, which represents water flow through hydroelectic dams. The ecoin-
vent database groups hydroelectric facilities into two process categories, “reservoir”
and “run-of-river”. These categories have reported elevation drops �z
i,j
= 0.05 [km]
and �z
i,j
= 0.01 [km], respectively. With this data it is possible to calculate the
potential exergy extracted from the flowing water. Therefore the matrix Bkey
con-
structed for the calculation of gravitational potential exergy consists of a single key
row, and a number of key processes equal to the number of hydroelectric generation
processes in B.
3.6 Kinetic exergy
The equation for calculating the kinetic exergy of a inventory matrix G is:
B
ke
=X
i
X
j
m
i,j
✓(v
i,j
� v
0
)2
2
◆=
X
i
X
j
m
i,j
✓�v
2
i,j
2
◆[MJ] , (3.23)
where Bke
[MJ] is the total kinetic exergy of the modeled system, mi,j
[kg] is the mass
of the i
th substance in the j
th process, vi,j
⇥km
s
⇤is the velocity of the i
th substance
in the j
th process, and v
0
⇥km
s
⇤is the velocity of the reference environment, which in
this study is assumed to be the stationary surface of the earth.
3.6.1 Reduction of matrix size
Kinetic exergy, like potential, chemical, and physical exergy, applies only to flows of
mass emitted to or drawn from the environment. In theory, Equation 3.23 applies to
every mass flow in G, as all flows are crossing a boundary between the technosphere
and the ecosphere, and thus by definition have some velocity v
i,j
> v
0
. However, in
34 CHAPTER 3. EXERGETIC LCA IMPLEMENTATION
Elevation data for most rows and processes is absent in the ecoinvent database.
Therefore the output and input elevations zi,j
[km] for most substances in Bmass
are
assumed to be sea level, such that �z
i,j
= 0 [km] and b
pe,i
= 0hMJ
kg
i.
The one exception to this assumption is the row “Water, turbine use, unspecified
natural origin”, which represents water flow through hydroelectic dams. The ecoin-
vent database groups hydroelectric facilities into two process categories, “reservoir”
and “run-of-river”. These categories have reported elevation drops �z
i,j
= 0.05 [km]
and �z
i,j
= 0.01 [km], respectively. With this data it is possible to calculate the
potential exergy extracted from the flowing water. Therefore the matrix Bkey
con-
structed for the calculation of gravitational potential exergy consists of a single key
row, and a number of key processes equal to the number of hydroelectric generation
processes in B.
3.6 Kinetic exergy
The equation for calculating the kinetic exergy of a inventory matrix G is:
B
ke
=X
i
X
j
m
i,j
✓(v
i,j
� v
0
)2
2
◆=
X
i
X
j
m
i,j
✓�v
2
i,j
2
◆[MJ] , (3.23)
where Bke
[MJ] is the total kinetic exergy of the modeled system, mi,j
[kg] is the mass
of the i
th substance in the j
th process, vi,j
⇥km
s
⇤is the velocity of the i
th substance
in the j
th process, and v
0
⇥km
s
⇤is the velocity of the reference environment, which in
this study is assumed to be the stationary surface of the earth.
3.6.1 Reduction of matrix size
Kinetic exergy, like potential, chemical, and physical exergy, applies only to flows of
mass emitted to or drawn from the environment. In theory, Equation 3.23 applies to
every mass flow in G, as all flows are crossing a boundary between the technosphere
and the ecosphere, and thus by definition have some velocity v
i,j
> v
0
. However, in
3.7. RADIATIVE EXERGY 39
3.7 Radiative exergy
The equation for calculating the radiative exergy in an inventory matrix G is:
B
rad
=X
i
X
j
e
i,j
A
i,j
t
i,j
1� 4
3
T
0
T
i,j
+1
3
✓T
0
T
i,j
◆4
![MJ] , (3.36)
where B
rad
[MJ] is the radiative exergy content of G, ei,j
⇥MJ
m
2s
⇤is the insolation
incident on the surface of the transformed land i from process j, Ai,j
[m2] is the area
of land transformed or occupied, ti,j
[s] is the duration of occupation, Ti,j
[K] is the
temperature of the emitting body, and T
0
[K] is the temperature of the reference
environment.
3.7.1 Reduction of matrix size
In this study radiative exergy calculations are applied strictly to changes in the
amount of solar radiation available to the environment. Specifically, changes in the
available solar radiation arise in conjunction with changes in land use. A process j
within the economy may transform or occupy a portion of the earth’s surface, shifting
the spatial boundary of the technosphere to encompass land formerly contained in
the ecosphere, or the converse. Alternatively a process may transform an area of
land already contained within the technosphere in such a way as to alter its radiative
properties. The ecoinvent database contains information of land transformations and
occupations associated with all relevent processes. For this analysis only land trans-
formation or occupation rows within B are considered for the calculation of radiative
exergy. After reduction, the matrix Bkey
contains 97 rows and 10,107 columns.
3.7.2 Solar exergy methods
Several methodologies have been developed in the scientific literature to calculate the
radiative exergy drawdown associated with changes in land use, as part of larger exer-
getic analyses of natural resources. These include cumulative exergy demand (CExD)
[19] and cumulative exergy extraction from the natural environment (CEENE) [18],
42 CHAPTER 3. EXERGETIC LCA IMPLEMENTATION
a) b)Before land transformation. After land transformation.
Techno
Eco
Techno
Eco
Eco
Techno
Techno
Techno
Chem. Ex.
Chem. Ex.
Rad. Ex. Rad. Ex.
Figure 3.11: Radiative exergy associated with land-use changes, cumulative exergyextraction from the natural environment method (CEENE).
3.8 Nuclear exergy
3.8.1 Reduction of matrix size
The intervention matrix B contains a number of radioactive substances emitted to
air, soil, and water. However the method for calculating nuclear exergy outlined
in Section 2.7 applies only to species used in electricity generating fission reactions.
Therefore the matrix B was reduced to include only those rows containing 235U,233U,
or 239Pu. After reduction, the matrix Bkey
contains 4 rows and 10,107 columns.
3.8.2 Calculation
The nuclear exergy of fission for a generic inventory matrix G is calculated as:
B
nuc
= 1.93x107X
i
m
i
M
i
[MJ] , (3.39)
Nat. res.
Wastes
Product T, p, ΔG, yi, z, v T, p, ΔG, yi, z, v
T, p, ΔG, yi, z, v
Process
A process takes in exergy in natural resources and other products, outputs exergy as
product and wastes
Other inputs T, p, ΔG, yi, z, v
Env. T0, p0, yi0, z0, v0
