# Raphael Fonteneau

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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 References [1] Wikipedia, Feu, Domestication par l'Homme [2] Auzanneau, M. (2011). 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