Raphael Fonteneau

Energy stories, equations
and transition
Une histoire d'énergie:
équations et transition
Sustainable Energy
March 8th, 2016
Raphael Fonteneau, University of Liège, Belgium
@R_Fonteneau
Energy Stories
Chenspec via Wikipedia
Fiesco via Wikipedia
Inconnu via Wikipedia
Mosaique du Grand Plalais, Constantinople via Wikipedia
Andrei Nacu via Wikipedia
Jacob van Ruisdael via Wikipedia
Hendrick Cornelis Vroom via Wikipedia
Diderot - D’Alembert via Wikipedia
Wikipedia
Hartmut Reiche via Wikipedia
Eric Kounce via Wikipedia
Trajectories of Societies
Johanna Pung via Wikipedia
Trajectories of Societies
Energy
Society
2. Energy <-> Economy
•
Recent research in Economics has shown that:
•
The empirical elasticity (measured from time series among
OECD countries over the last 50 years) of the consumption of
primary energy into the GDP is about 60%, which is 10 times
higher that what is predicted by the Cost Share Theorem
Elasticity can be quantified as the ratio of the percentage change
in one variable to the percentage change in another variable
•
There is a causality link between the consumption of primary
energy and the GDP in the direction Energy -> GDP
$€
Variation lissée de la consommation mondiale de pétrole (rouge) et du PIB par
Variation of(bleu).
the world
oil consumption
(red)
and pour
GDP per
inhabitant
(blue)
- Data
from
the the
personne
Source
World Bank
2013
le PIB,
BP Stat
2013
pour
le pétrole
World Bank for GDP and BP stat for energy
Source (in French): Jean-Marc Jancovici, « L’économie aurait-elle un vague rapport avec l’énergie? », LH Forum,
27 septembre 2013
The challenge
Non renewable
> 80% - < 20%
Renewable
Equations and
Transition
ERoEI
•
ERoEI for « Energy Return over Energy Investment » (also
called EROI) is the ratio of the amount of usable energy
acquired from a particular energy resource to the amount of
energy expended to obtain that energy resource:
U sable Acquired Energy
EROI =
Energy Expended
•
The highest this ratio, the more energy a technology brings
back to society
•
Notation : 1:X
D
F
I
D
-
5
9
7
1
7
st
Source: EROI of Global Energy Resources - Preliminary Status and Trends - Jessica Lambert, Charles Hall, Steve Balogh, Alex
Poisson,
and7:Ajay
University
of New
York,
College of
Environmental
and Forestry
Report 1 - Revised
Figure
TheGupta
“NetState
Energy
Cliff”
(figure
adapted
from
LambertScience
and Lambert,
in preparation
[3] and
Submitted - 2 November 2012 DFID - 59717
Murphy et al. 2010 [71]) As EROI approaches 1:1 the ratio of the energy gained (dark gray) to the en-
s in the order of hundreds of years:
Modelling the transition?
T ⇠ 100
500
A the
discrete-time
model of from
the deployment
of
egarding
energy produced
non-renewable
sources
•
« renewable energy » production capacities
ch year,
a
quantity
of
non-renewable
energy
is
available:
• Budget of non-renewable energy
8t 2 {0, . . . , T
1}, Bt
0.
assume 9r
that>such
is
0, 9⌧a quantity
> 0, 9t0of2 energy
R : 8t is
2 net
{0, (this
. . . , Tassumption
1},
he chapter). By renewable energy, we mean fossil
(coal,
(t tenergy
0)
⌧
1
e
also nuclear energy (Uranium Bfission).
For
clarity
here,
we
=
⌘2
⇣
t
(t
t
)
0
r
rate the different types of energy production
technologies
from
⌧
1+e
rces. The evolution of the quantity of available non-renewable
To each technology is associated a production capacof
energy
R
:
n,t
rgy
from
renewable
origin
y of energy Rn,t:
Modelling
the
transition?
sources is available. To each technology is associated a producti
N
{0,
, Tdifferent
R
N},
},8t
8t 2a{0,
T
1},1},
Rn,t
n,t 0. 0.
ume
that
set...of. ., N
technologies
for producing energy
y
producing
a
quantity
of
energy
R
:
us
(non-comprehensively)
mention
biomass,
hydron,t
• Set of renewable energy
us (non-comprehensively)
mention
biomass,
hydroproduction
technologies:
photovoltaic
panels.
Two
main
parameters,
the
exhotovoltaic
panels.
Two
main
parameters,
the
ex8neach
2 {1,
.
.
.
,
N
},
8t
2
{0,
.
.
.
,
T
1},
R
0.
faracterize
the deployment
of
energy
production
means
is
modeled
n,t
of these technologies:
racterize
each
of
these
technologies:
r:
us (non-comprehensively)
mention biomas
Nthese
}, 8t•technologies,
2Characteristics
{0, . . . , T let1},
0.
n,t
},
8t
2
{0,
.
.
.
,
T
1},
0.
n,t
ty,
wind
turbines
or
photovoltaic
panels.
Two
main
parameters
1, . . . , N }, 8t 2 {0, .ERoEI
. . , T n,t1}, R
=
(1
+
↵
)R
n,t+1
n,t
n,t
0.
ifetime and ERoEI characterize
each
of
these
technologies:
ERoEI
0.
y production means is modeled n,t
using a
wth parameter
may
be
negative:
vided
section
2.
The
expected
lifetime
parameter
•inDeployment
strategy
8n 2 {1, . . . , N }, 8t 2 {0, . . . , T 1},
0.
n,t
of equipment
allowing
energy
production.
Noteparameter
that
ded
in section
2. The
expected
lifetime
ERoEIn,t 0.
21},
{1,R
.n,t+1
. . , N=
},allowing
8t
{0,
. . .n,t
, T production.
1},
↵n,t 2 Note
[ 1, 1[
(1
+2↵
)R
sider
fluctuation
and
storage
issues
associated
with
n,tenergy
of
equipment
that
nider
practice,
providing
storage
capacities
or
technolo- with
fluctuation
and
storage
issues
associated
ion of ERoEI is provided in section 2. The expected lifetime p
e{0,
technologies:
. . . , T 1}, ↵n,t 2 [ 1, 1[
nt becomes
obsolete
to .be
(see
later
in
the
8n 2 {1,
. . . , Nand
}, 8thas
2 {0,
. . ,replaced
T 1}, M
0
n,t
ptions regarding this energy cost).
{1,
.
.
.
,
N
},
8t
2
{0,
.
.
.
,
T
1},
C
(R
,
↵
)
0
n,t
n,t
n,t
Energy costs for growth and long-term replacement
Modelling the transition?
of this quantity of energy is to formalize the energy cost that ha
g-term replacement
nntroduce
equipment
becomes
obsolete
and
has
to
be
replaced
(see
later
thealso
energy
cost associated
with
the growth
of thefor
production
c
this
cost
incorporates
the
energy
required
mainten
nd
net
energy to regarding
society this energy cost).
few
assumptions
of
technologies:
•the
Energy
costsoffor
growth
and long-term
replacement
me
of
equipment.
We
also
introduce
the energy
cost assoc
edrenewable
with
the
growth
the
production
capaci-
replacement
of the the
production
means:
notations,
we
define
total
energy
at year
t:
8n 2 {1, . . . , N }, 8t 2 {0, . . . , T produced
1}, Cn,t (R
,
↵
0
n,t
n,t )
energy and net energy to society
...2
, T{1, 1},
↵n,t.). . , T0 X
8n
...C
,N
8tn,t
2, {0,
0
N 1}, Mn,t
n,t},(R
assume that this cost also incorporates the energy required for maint
8t
2
{0,
.
.
.
,
T
1},
E
=
B
+
R
t
t
n,t
ngprevious
the lifetime
of the equipment.
We total
also introduce
the energy
notations,
we define the
energy
produced
at cost
yearasso
t:
n=1
porates
the
energy
required
for
maintenance
quantity
of
energy
is
to
formalize
energy cost that has
•
Total
energy and
energy tothe
society
e long-term
replacement
of net
the production
means:
N
We also
introduce
the energy
pment
becomes
obsolete
andcost
has associated
to be replaced
(see later in
X
net
energymeans:
available
to
society:
8n
2
{1,
.
.
.
,
8t 1},
2 {0,
. . ,B
Tt +1}, MR
8t
2
{0,
.
.
.N, T},energy
Ecost).
oduction
n,t
t. =
n,t 0
sumptions regarding this
n=1
!
N
X
2
{0,of. this
. . , Tquantity
1}, M
role
of n,t
energy0is to formalize the energy cost that ha
.efine
,when
T the
1},
S
=
E
C
(R
,
↵
)
+
M
t
t
n,t
n,t
n,t
n,t
net energy
available
to society:
equipment
becomes
obsolete
and has to be replaced
(see later
y and net energy to society
n=1
onstraints on the quantity of energy invested for energy prod
e quantity
of energy
invested for
production
ssume
that the
energy investment
forenergy
developing,
maintaining a
roduction means from renewable sources cannot exceeds a give
nergy
investment
developing,
maintaining
tal energy.
In otherfor
words,
this assumption
meansand
thatreplacing
the ratio
yfrom
over
total
energy
has
to
remain
above
a
given
threshold.
For
renewable
sources
cannot
exceeds
a
given
fraction
of
• Constraint on the quantity of energy invested for
that:
her
words,
this production
assumption means that the ratio net energy to
energy
gy has to remain above a given threshold. Formally, we as1
8t 2 {0, . . . , T 1}, 9 t : Cn,t (Rn,t , ↵n,t ) + Mn,t 
Modelling the transition?
t
1
.e ,following,
T 1}, 9 we
Cn,t (Rby
↵n,t ) +threshold”
Mn,t  such
Et a paramet
t : denote
n,t ,“energy
t
t is motivated by research investigation showing that, if a soc
gh
proportion
of
its
energy
for
producing
energy,
then
less
ener
denote by “energy threshold” such a parameter. This conother society needs, which may result into a decrease of the g
y research investigation showing that, if a society invests a
re [Lambert et al. (2012)].
its energy for producing energy, then less energy is dedicat-
Cn,t (Rn,t , ↵n,t ) =
⇢
n,t ↵n,t Rn,t
if ↵n,t
0 else
0
Modelling the transition?
costs allowing a given production capacity producing energy
fetime• is
done assumptions
initially. This results into the following equaFurther
Energy cost for growthn,t
is proportional to growth, and
8t 2 {0, . . . , done
T 1},
n,t =
initially:
2 {0, . . . , T 1}, 9µ > 0 : M (R ) = µ R
•
n,t
ERoEI
n,t
n,t
n,t
n,t
n,t
n,t
Cn,t (Rn,t , ↵n,t ) =
↵n,t Rn,t if ↵n,t
EI parameter, we get the following
ERoEIequations:
n,t
0
1
cost
associated
with
the
long-term
replacement
of production
• Long-term
replacement
and (ii)
N }, 8t 2 {0,
. . . , T 1},
µn,t = cost is (i) proportional
ERoEI
(i) annualized
and (ii) proportional
to the n,t
quantity of energy
annualized
uced:
1
Mn,t (Rn,t ) =
ERoEIn,t
Rn,t
ic panelsrenewable
in the worst
case
configura-energy probetween
and
non-renewable
depletion
of non-renewable
is initially
dhevariables
with
respect
to
the energy
total
energy
at
mbert
et
al.
(2010)]
which
provides
two
12)]:
s the current
situation
2014 [British Petroleum
etween
renewable
andofnon-renewable
energy pro1.4
1.8
Energy for energy
Energy to society
Total energy
Renewable
Non−renewable
1.2
Energy for energy
Energy to society
Total energy
Renewable
Non−renewable
1.6
PV
I1,t
ERoEI
the
current
situation
E=
=
1
min = 6 of 2014 [British Petroleum
0
1.4
1
Normalized energy
Normalized energy
aic Bpanels
in the worst case configura0 = 0.85E0
c012)]:
panels in of
thenon-renewable
best case configuration
depletion
energy is initially
= 0.85E0and
eenB
non-renewable
energy toproed
by0renewable
photovoltaic
is initially assumed
be
P panels
V
EI
=6
1,t = ERoEI
e
current
situation
P Vmin of 2014 [British Petroleum
nergy
mix:
I1,t = ERoEImax = 12
d by photovoltaic panels is initially assumed to be
aic
in the0best case configuration
Rpanels
= 0.01E
ergy
mix:
1,0
he average of these two values, 9i.e.:
B]:0 = 0.85E0
9
R1,0corresponds
= 0.01EP0 to
ately
current proportion of enerV the
ERoEI
=
9
N
Fig.
2. Scenario “peak at time t=0”
1,t
EIX
=
ERoEI
=
12
1,t
max
plus=wind
turbines
in
the world
total energy
photovoltaic
panels
is
initially
assumed
to be
=ypanels
RNn,0
0.14E
0
ies
producing
energy
from
renewable
sources
are
X
ately
corresponds
to
the
current
proportion
of
enery
mix:
n=2
es
of
PV panels
is still
discussed
in the
the
average
of
these
two
values,
i.e.:
el,
i.e.:
=
R
=
0.14E
,t
n,0 turbines 0
panels
plusthat
wind
the world
12)]), and
(ii) it is veryinlikely
that total energy
t1,0
may
be
dedicated
to growing
enn=2
Res
=
0.01E
producing
energy
from
renewable
sources are
0
uture.
In
all
configurations
considered
}, ERoEI1,t = 9
el,
i.e.: parameter equal to 20:
lifetime
that
may
be dedicated
to growing
y tcorresponds
to the current
proportionenof ener=
14
ues of PV panels is still discussed in the
1},
20 turbines in the world total energy
nels plus
wind
1,t =
2012)]), and that (ii) it is very likely that
producing
energy
fromreported
renewable sources are
is motivated
by results
eldfuture.
In all configurations
considered
.e.:
own
et al., this value
14
tby=Lambert
a},lifetime
parameter
equal to 20:
1.2
0.8
0.6
1
0.8
0.6
0.4
0.4
0.2
0
0
50
100
150
200
250
300
0.2
0
350
0
50
100
150
200
Time t
300
350
400
450
Fig. 3. Scenario “plateau at time t=0”
1.6
2
Energy for energy
Energy to society
Total energy
Renewable
Non−renewable
1.4
250
Time t
Energy for energy
Energy to society
Total energy
Renewable
Non−renewable
1.8
1.6
1.4
1
Normalized energy
Normalized energy
1.2
0.8
0.6
1.2
1
0.8
0.6
0.4
0.4
0.2
evelop and sustain social amenities
ociety
Maslow
pyramid”, such as
Constant
growth
1}, is
= 20
1,tmotivated
hold
results
“Pyramid
of Energetic
Needs”
in reported
if possible,
else
by
Fig.et4. al.,
Scenario
at time t=20”
max admissible
shown
by Lambert
this“peak
value
0
0
50
100
150
200
Time t
250
300
0.2
350
0
0
50
100
150
200
250
300
350
400
450
Time t
Fig. 5. Scenario “plateau at time t=20”
12
Modelling the transition
Increasing
theproduction
ERoEI parameter
of the •renewable
energy
capacities is boosted by the availability of
non-renewable resources.
As a second observation, we notice that the depletion scenario has an influence
on the maximal level of production that can be reached during the transition phase.
However, one can compute that it does not affect the steady-state production level,
which is exactly the same in the four scenarios, and function of the ERoEI of the
photovoltaic panels.
To illustrate the influence of the ERoEI parameter on the levels of energy production, we give in Figure 8 a last run of MODERN for which we consider a linear
increase of the ERoEI parameter from 9 to 12 between time 0 and the time horizon
(the growth scenario is the same as before, 10% annual growth):
1.4
Energy for energy
Energy to society
Total energy
Renewable
Non−renewable
1.2
Normalized energy
1
0.8
0.6
0.4
0.2
0
0
50
100
150
200
250
Time t
8t 2 {0, . . . , T
1}, ERoEI1,t
t
= 9 + (12
T
9)
Epilogue
PhR61via Wikipedia
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