# 4.1 Individual Infrastructures

IEA (2002) provides estimates of EROI, ', and �1 in table 8.2, ...gure 8.8, and table 8.4, respectively. Moreover, it assumes that T = 30 years for all infrastructures. From these E values we can back-calculate<sup>We subsequently</sup> Pnp'T<sup>and h (and hence q) using (2) and (5).</sup> employ reasonable estimates of the required construction time t<sup>~</sup> for new generating plants, set the plowback ratio � to .2, and use (11) and (12) to estimate � and �2: All of these values are presented in Table 1.

With a 20% plowback (i.e. � = :2), oil and gas-...red plants can attain 84% annual expansion growth rate, coal-...red 73%, nuclear 58%, hydro 23%, wind 2% and PV 1%. Thus, conventional fossil fuels (oil, natural gas, coal), nuclear power, and to a lesser extent hydro, show potential to support rapid growth. Wind and especially PV, on the other hand, seem quite constrained. This is surprising in light of wind’s EROI being as large as coal’s and its O&M plowback fraction h being smaller than that of coal. To understand this outcome is it necessary to examine the ...xed vs variable components of EROI in (2). The ...xed component for wind, representing the fraction of gross production expended for initial emplacement, is over 25 times larger than that of coal’s. This also is re‡ected in the comparison of their energy payback period �1; whose computed value is 3.39 years for wind and only 0.15 years for coal.

The doubling time �2, again with a 20% plowback, is 1.1 years for oil and gas plants, 1.3 years for coal, 1.5 years for nuclear, 3.3 years for hydro, 28.5 years for wind, and 82.9 years for PV systems. Thus, the ability of wind and PV systems to rapidly scale up their production by bootstrapping their own energy appears to be limited. Even if all the energy produced by these systems was plowed back (� = 1:0) to support their scale up, their expansion rates would still be well-below those achieved by fossil fuel and nuclear plants with a plowback of just 20%. For example, if we set � = 1:0; then we obtain: � = :21; �2 = 3:29 for wind; and � = :14; �2 = 4:88 for PV. According to these estimates, which are based on pre-2002 technologies, under a 100% plowback, wind power could attain an annual growth rate of 23% and double its capacity every 3.3 years. However, global wind power achieved 29.2% annual growth rate in 1998, 41.7% in 1999, 31.7% in 2000, 34.8% in 2001, and 28.2% in 2002 (WWEA, 2009). Clearly, that type of expansion could not have been achieved without an energy subsidy from conventional fossil fuels and nuclear plants.

It is also important to note and interpret the signi...cant di¤erence between the estimated values of the energy payback period �1 and doubling time �2; especially for wind and PV. According to Table 1, the energy payback period �1 for a PV system is 4.76 years–although, as it will be noted below, in the last few years this number has been shortened considerably due to technological change. Under a 20% plowback constraint, it will take it another 5�4.76 or 23.80 years to produce enough energy to double its emplaced infrastructure. Thus, it will take a PV system 28.56 years in total to replicate itself. However, given that the system’s expected lifetime is 30 years, by the time it produces the required amount of energy to double its capacity, the system becomes largely obsolete and requires replacement. The ~ system’s growth will be very slow–indeed in (12),<sup><u>�'(1 �</u>h)1thus�issmall.</sup> q T<sup>and</sup> 12