Exergy Resources I:
Solar exergy flows and simple conversions
ENERGY/EE 293 B
Fundamentals of renewable energy
processes
1. Nature of solar energy flows
– Magnitudes
– Quality
– Variation across globe
2. Conversion to thermal energy gradients
3. Conversion to precipitation
2
Lecture overview
3Solar exergy flows
Source: Hermann (2006)
4Solar exergy flows
Source: Hermann (2006)
Nature of solar energy flows
• Solar energy flows dominate all other
renewable energy flows
• Solar energy flows are vastly in excess of
human energy demand
• Solar energy drives most secondary exergy
accumulations
– Vastly different refresh rates (e.g., PV vs. fossil)
Worked problem: Solar exergy flux to earth
rs
reo re
Observed solar irradiance – Top of atmosphere
Source: http://earthobservatory.nasa.gov/Features/ACRIMIII/
• Radiation (electromagnetic) exergy
• T0 << T, so solar radiation is high quality
• Solve for sun and earth
– T = 5778 K and T0= 298 K
– Qem = 0.93
• Scattering reduces quality received
• Use this for radiative energy transfer between two bodies
(not for energy transfer via conduction or convection)
8
Radiation exergy from the sun
ememem EQX =
4
00
3
1
3
41 ÷
ø
ö
ç
è
æ+-=
T
T
T
TQem
9Effect of scattering and differential absorption
Source: http://oceanworld.tamu.edu/resources/ocng_textbook/chapter05/Images/Fig5-2.htm
Angle of sunlight with latitude
At higher latitudes, m2 at of area normal to sun at atmospheric boundary
projects to larger area at land surface.
Projection effect: The same light is spread over larger area.
Air mass effect: The light is scattered more thoroughly as it moves through
atmosphere
1 m2
1 m2
1367 W
1367 W
Angle α
1 m
Length = 1/sin(α)
At α = 15 degrees:
As/Acr ≈ 4
Resulting insolation - World
• Overall pattern
dominated by
projection/air mass
effect
• Local variability is
strong
– Cloud cover in
Amazon results in
insolation 60% of
expected
– Weather patterns
in Antarctica keep
interior relatively
cloud free (top) MJ/m2/day 0 30.6
Source: Da Rosa, 2009, http://visibleearth.nasa.gov/view_rec.php?id=1683
12
Ocean thermal gradients
Source: Hermann (2006)
• Water is warmed in the tropics, moves to
poles, where it cools and sinks
– Currents driven by winds and density differences
• Results in ocean thermal energy gradient
• Because reference state is the surface water,
cold bottom water is a thermal exergy
resource (as a heat sink)
13
Conversion of solar flux to thermal energy
14
Heat transfer to poles
MJ/m2/day 0 30.6
15
Thermal effects of ocean circulation
Source: Smithsonian National Museum of Natural History (http://forces.si.edu/arctic/04_00_16.html)
• Bulk of poleward heat transfer occurs in
atmosphere, except near equator
16
Poleward heat transfer by air and water
Source: Trenberth and Caron (2001)
• Thermal exergy of a given amount of matter
• Assume the matter starts at reference
temperature T0, and add an increment of
thermal energy:
17
Thermal exergy of matter above environmental temperature
dXth =QthdEth Qth = 1−
T0
T
"
#
$
%
&
' dXth = 1−
T0
T
"
#
$
%
&
'dEth
Xth = 1−
T0
T
"
#
$
%
&
'dEth
T 0
T
∫ Xth =mcp T −T0 −T0 ln
T
T0
"
#
$
%
&
'
"
#
$$
%
&
''
Source: Szargut (various), Dincer and Rosen (2013). Some assumptions req. in derivation.
• Thermal exergy of large bodies of matter at different
temperatures
• We assume that bodies of matter are enormous so
neither changes temperature appreciably (e.g., Tc and
Th remain the same), what is the work potential of heat
transfer between Tc and Th?
– Unavoidable thermodynamic losses are large for low ΔT exergy flows
18
Thermal exergy of ocean temperature gradients
Qth = 1−
T0
T Xth =QthEth
Xth =mcp,avg Th −Tc( )1−
Tc
Th
Hermann eq. 12:
This equation only holds for two heat
transfer between two large reservoirs,
each of unchanging temperature
• Differential form applies if a finite amount of
material is reduced in temperature toward
reference conditions
– Every additional unit of thermal energy you
remove comes at a lower T = lower Q. Hence,
integral form
– Example: Cooling of a finite body toward T0
• Constant T form applies if energy is always
removed at Th and Th never drops
– All energy transferred has same Q factor
– Example: Removing heat from a very large body
19
Differential form vs. constant T form
20
Constant T form of thermal exergy equation
Hot
Cold
Th
Tc
Qh
Qc
W
For a Carnot cycle:
Qc/Tc = Qh/Th
so:
η = W/Qh
= (Qh-Qc)/Qh
= 1-Qc/Qh
= 1-Tc/Th
Differential form Constant T form
Hot
Th
T0
Time
Hot
T0
Time
Th
Cooling a finite body
to T0, extracting
work along the way
Pulling energy Qh from
hot body that always
remains at Th
“How much work
potential in a stream
of hot gas?”
“What is the
efficiency of an ideal
engine run between
two very large
reservoirs at Th and
Tc?”
21
OTEC – Ocean thermal energy conversion
Source: Hermann (2006). Photo is OTEC system in Hawaii.
• Ocean thermal energy
conversion relies on
ocean temperature
differences to
generate work
• Low-boiling point
working fluids (e.g.,
refrigerants) are used
in closed cycle systems
• Pros: Lots of energy
available: 2000 TW
• Cons: Low work
potential: ΔT ≈ 20 °C
22
Quality of thermal gradients
Source: Adapted from Hermann (2006)
23
“Cold works too”
Source: University of North Texas, physics and engineering dept.
See: da Rosa (2009) Section 3.9
Cryogenic heat engine
“Fuel” (exergy store) is
cold liquid nitrogen
Heat for heat engine
comes from
atmosphere
• Costs of a heat engine are proportional to
amount of fluid moved
– Capital investment increases
– Pumping costs are large in comparison to work
extracted (parasitic load)
– Maintenance and wear scales with activity
– Ocean is an unforgiving environment
24
Difficulties of working with low ΔT
25
Precipitation
Source: Hermann (2006)
• Evaporation and transpiration
(evapotranspiration) of water moves
enormous masses of water into the
atmosphere as vapor
– Rain flux downward = 18 x 1012 g/sec
– Evaporation is (on average) in balance
26
3. Exergy conversion via precipitation
• Exergy of precipitation is stored as
gravitational and chemical potential exergy
– Gravitational because mass is lifted above the
surface of the earth
– Chemical potential because concentration of
dissolved ions is sharply reduced in fresh water
27
Conversion of energy during precipitation
• Gravitational exergy
– Z0 is reference state, in this case the ocean (sea level)
– Z depends on where you are measuring the exergy
– Clouds, top of Mount Everest, average height of rainfall?
28
Gravitational exergy of precipitation
)( 0zzmgEX gpegpe -==
29
Chemical exergy has multiple parts
• Chemical exergy
– Change in enthalpy: Δh represents the “bond potential”
due to changes in the energy of the system due to changes
in chemical bonds
– T ΔS represents the “degrees of freedom” potential, or the
entropic change upon the reaction occurring
– Δh-T ΔS = Gibbs free energy of formation associated with
generating a substance from reference species in reference
environment
• Maximum work available from a reaction at constant temperature
and pressure
– RT0ln(yi/y0) is the “diffusive” potential due to the
concentration gradients between the system and the
environment
30
Chemical exergy step-by-step
m = mass of species or mixture [kg]
ψ = specific chemical exergy [MJ/kg]
!" =## 1# ' #' !",#% MWi = Molecular weight of species i in mixture [g/mol]yi = Mole fraction of species i in mixture [mol/mol tot]0i = chemical potential of species i at standard conditions [kJ/mol]
!" = $ !"
!",#% = −∆&% + % ln #% Δg = Change in the standard state Gibbs free energy of reactionR = Universal gas constant = 8.314 J/mol-kT0 = reference temperature (25C)yi = mole fraction of species i in mixture
y0 = mole fraction of species in reference environment
For simple reactions, tabulated gibbs free energy of
formation data can be used to compute delta g, otherwise:
∆&% = ∆&ℎ% − %∆& Δh = Change in the standard state enthalpy of reactionR = Universal gas constant = 8.314 J/mol-kyi = mole fraction of species i in mixture
y0 = mole fraction of species in reference environment
31
Example: Oxidizing methane
Example: Oxidizing 1 mol of methane
CH4 + 2O2 => CO2 + 2H2O (g)
* For simplicity all products and
reactants at 25 °C in gaseous phase
(in reality some water will condense at
25 °C)
Air Reversible
Reactor
Reversible
unmixer
Reversible
mixer
CH4
2O2
CO2 + 2H2O (g)
Our thought experiment:
• Use “perfect” reversible
machines to make CH4 out of
components of reference
environment
• “How much work did that
take?”
32
Example: Oxidizing methane
Example: Oxidizing 1 mol of methane
Look up Gibbs data for species in reaction
Source: Cengel and Boles (2006)
Species h0f
[kJ/mol]
g0f
[kJ/mol]
s0
[kJ/mol-K]
CH4 -74.850 -50.790 0.186
N2 0 0 0.191
O2 0.00 0.00 0.205
CO2 -393.520 -394.360 0.213
H20 (g) -241.820 -228.590 0.188
H20 (l) -284.83 -237.18 0.069
Species y0 in air
CH4 NA
N2 0.7651
O2 0.2062
H20 (g) 0.019
Ar 0.0094
CO2 0.0004
Define reference env.
T = 298 K
P = 100 kPa = 1 atm
Molar conc:
33
Mixing and unmixing gases from atm
'#()*+ = % ln #%
Example: Oxidizing 1 mol of methane
CH4 + 2O2 => CO2 + 2H2O (g)
* For simplicity all products and
reactants at 25 °C in gaseous phase
(in reality some water will condense at
25 °C)
Species y0 in air Wmix for
pure gas
[kJ/mol]
CH4 NA -
N2 0.7651 0.66
O2 0.2062 3.91
H20 (g) 0.019 9.82
Ar 0.0094 11.57
CO2 0.0004 20.11
Minimum work
of separation:
yi: Concentration desired
y0: Reference concentration
34
Example: Combusting methane
Example: Oxidizing 1 mol of methane*
CH4 + 2O2 => CO2 + 2H2O (g)
Look up Gibbs data for species in rx
Source: Cengel and Boles (2006)
Species h0f
[kJ/mol]
g0f
[kJ/mol]
s0
[kJ/mol-K]
CH4 -74.850 -50.790 0.186
O2 0.00 0.00 0.205
CO2 -393.520 -394.360 0.213
H20 (g) -241.820 -228.590 0.188
H20 (l) -284.83 -237.18 0.069∆&% = #,)-. %/ − #)*0!1 %/∆&% = −394.360 − 2 ∗ 228.590 − −50.790 + 0 =
= 800.75 kJ/mol
* For simplicity all products and
reactants at 25 °C in gaseous phase
(in reality water will partly condense at
25 °C)
35
Example: Combusting methane
Air Reversible
Reactor
Reversible
unmixer
Reversible
mixer
CH4
2O2
CO2 + 2H2O (g)
Spend: 800.8 kJ/mol
Spend: 20.1+2*9.8 = 39.7 kJ/mol
Get back: 2*3.9 = 7.8 kJ/mol
Our machine to make
methane would spend:
800.8 + 39.7 - 7.8 = 832 kJ/mol
So, exergy content of methane:
832 kJ/mol = 52.0 MJ/kg
• Chemical exergy
– Assume no chemical reactions, just distillation of water
– We only have RT0ln(yi/y0), the diffusive potential due to
the concentration differences between the system and the
environment
36
Chemical exergy of precipitation
chch mX y= ÷÷
ø
ö
ç
ç
è
æ
=÷÷
ø
ö
çç
è
æ
=
saltw
freshwi
ch y
y
RT
y
yRT
,
,
0
0
0 lnlny
37
Precipitation exergy diagram
Gravitational
Xg
Chemical
Xch
Gravitational
Xg
• Hermann, W. (2006). Quantifying global exergy
resources. Energy 31, 1349-1366
38
Further reading

欢迎咨询51作业君