Adjusting Energy Return on Investment (EROI) for Time

Nate Hagens wrote a post at The Oil Drum called Applying Time to Energy Analysis. Under standard EROI analyses, there is no recognition of time – if you cut down a tree, but couldn’t burn it for energy until 50 years from now, it would count the same in terms of EROI as if you could burn the tree, the day after you cut it down (except perhaps for the embedded energy in the shed where you needed to keep the log for 50 years).

There are a lot of reasons why energy that is not available for a long time might be less valuable. If nothing else, if energy is not available for a long time, it will be necessary to tie up capital in developing this source of energy.* Dennis Meadows of Limits to Growth fame has said that the limiting factor as we approach “Limits to Growth” is capital. If some types of energy production tie up capital disproportionately, this, in itself, is a problem, because it will limit total energy available to society. If these sources of energy are low EROI to begin with, this is a double hit.

A second issue is that we really don’t know how long we will be able to use any type of capital energy investment.* We know how long a wind turbine might last under a Business as Usual scenario, but we don’t know whether the entire system of which it is a part will last that long. For example, will the transmission system still be in good repair? We also don’t know whether we will be able to buy replacement parts for wind turbines that fail, many years from now, or if access roads will be open repair people to fix turbines needing repair.

Nate talks more abstractly about society’s preference for energy usable now, vs energy usable in the future, and looks at discount rates from various studies. He then calculates indicated discounted and undiscounted EROIs for various energy sources.

EROI time shifts

Figure 1. Time Shifts after Discounting by Nate Hagens

Based on Figure 1, the EROI for wind, solar PV, and corn ethanol all decrease, when time discounting is used. The effect is greater, the greater the discount rate.

Nate shows the various EROIs as if they are comparable to each other, but I am not entirely convinced of their comparability. To me, it makes sense to compare the EROI of one wind turbine with the EROI of another wind turbine (calculated by the same person, with the same formula), but I am less certain about the comparability among energy sources. Each of the EROIs is calculated at the point of generation. It seems like what one would really want to compare is the amount of energy required to deliver a particular source of energy to the user. Such a calculation would produce considerably lower EROIs for all of the energy sources, but especially for wind, if upgrading to the grid and electrical storage are required.

Nate shows graphically what the effect of discounting is. This may be helpful to get an idea of the relative magnitude of the adjustment. For wind, he first shows inputs and outputs, without discounting:

Figure 2. Wind turbine energy input/output timeline - undiscounted

He then shows how much impact discounting at 5% has on these flows:

Figure 3. Wind inputs and outputs from Figure 2, discounted at 5%.

He finishes by showing the much greater impact of discounting at 15% on the same flows:

Wind turbine energy input/output timeline - Discounted at 15%

Figure 4. Wind turbine energy input/output timeline - Discounted at 15%.

*This is not an issue raised by Nate Hagens.

About Gail Tverberg

My name is Gail Tverberg. I am an actuary interested in finite world issues - oil depletion, natural gas depletion, water shortages, and climate change. Oil limits look very different from what most expect, with high prices leading to recession, and low prices leading to inadequate supply.
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7 Responses to Adjusting Energy Return on Investment (EROI) for Time

  1. marty schoffstall says:

    Your comments are spot on, you definitely have to deal with the user delivery, i’d propose you have to abstract things in two ways, first heat vs electricity. then infrastructure availability, let’s start simply there with three classes: BAU, interstate-grid-down, grid-down. i’d also like to divide solar into two pieces: “individual rooftop” and “large grid attach”. (sorry for all the balls in the air)

    Now let’s think about: individual rooftop solar electric. whether BAU, or either grid down scenarios you probably have the same EROI in your graphic.

    Offshore gas: BAU little change. either grid down your EROI goes to zero.
    Wind: BAU little change. interstate grid-down for argument sake a 75% haircut, grid down is zero

    As an engineer I am always worried about step functions, one of my side jobs in the 90s on 3 continents was building backup power plants for tech. people loved NG, for those in cold climates or where substantial grid power was generated by NG, I would remind them that not only were they dealing with grid availability (NG grid) but also potential implications of a policy forcing function of heat vs their backup. Never going to happen they would say, diesel is too dirty. All those plants are still in place. But now we have countries as diverse as Pakistan and England in the past 12 months experiencing that terror.

    I’m a diesel guy. Nothing like local storage. I also have more confidence in the long term ability to fix diesel engines, generating diesel fuel is a bit harder. I’m hoping and praying that someone makes a commercial downdraft gasifier, my efforts have been less than successful. I’ve been testing diesel fuel every year for aging with treatment, i’m upto 12 years from a 1998 batch, i probably should start testing untreated.

    • You are right–there are a lot of little pieces.

      On the roof-top grid, it seems like most folks wouldn’t make very good use of theirs, if the grid goes down. First, they would have to get rid of the inverter, and run it directly to whatever appliances could use it, when it happens to be available. It might work for a few things, but not too many, I would guess. It would work for light bulbs, I would expect, but who needs a light bulb when the sun is shining? A few folks have battery back-up, but they don’t last very long before they need replacement.

      • marty schoffstall says:

        The battery issue is another tough one but i’d hope that deep cycle batteries would be in manufacturing reach, certainly standard lead acid should be.

        I’ve been wondering at what point the pure grid tie configurations that generally are installed might change to limited battery charging with inverter. Not yet that is for sure.

  2. majorian says:

    Nate, who should know better being a former investment banker, has got it wrong again because he left off the escalation/inflation price of energy e.
    Interest rates and discount rates are almost the same; a 5% discount rate is a 5.263% interest rate.
    Higher interest rates do increase the ‘simple payback’ period.
    For example, lets say you have a 1 kw wind project costing $1500 per kw which produces 2500 kwhs per year at 10 cents per kwh. The simple payback at current utility rates is 6 years; $1500/($.1 x 2500)=6.
    At an 1% interest rate the payback is 6 years but in a 8% interest rate environment
    the payback gets drawn out to ~9.5 years only if you ignore energy inflation.
    PB= log(1-SPB(1-(1+d)/(1+e))/log(1+e/1+d)
    If you project an 8% interest rate(a 7.36% discount rate) in a 2.8% price environment (current escalation of electricity prices); 1+.028/1+0736 =.957 k-factor would result in a revised payback of 7 years.
    Lets look at a situation where energy prices are rising faster say 10% than interest rates at 3%. That leads to a k-factor of 1.06796 and there the 6 year simple payback period would shrink to 5.5 years.
    If energy inflation and the discount rate are the same the simple payback equals the revised payback.
    If a rapid decline of fossil energy leads to rampaging consumer energy inflation it actually shortens the payback of renewables.
    OTOH, for oil and gas the situation is much worse.
    A gas peaker generator costs $500 per kw and runs 2500 hours per year at a rate of
    12cu.ft. per kwh and gas costs $.5 for 100 cu.ft. of gas . The object is to produce electricity at 10 cents per kwh.
    The return therefore is $.10-$.5 x 12/100 =4 cents per kwh x2500 =$100.
    So the simple payback is 5 years=$500/$100. However if the price of natural gas rises goes to $1 per 100 cu.ft. tand the price of electricity goes up to 11 cents per kwh
    (almost certain as most electricity comes from cheaper fueled coal and nuclear)
    then the return goes to -$250; ($.11-$1 x 12/100) x 2500 =-$250.
    and the generator goes silent regardless of the discount rate.

    • Don Millman says:

      You are quite right. It is always good to go back to fundamentals, and the most basic observations on interest rate/discount rate were made by Eugen Bohm-Bawerk more than a hundred years ago. He emphasized capital being needed because of the “roundaboutness” of production being more efficient than production in the absence of capital. The supply of physical capital depends largely on the interest/discount rate. Without an adequate interest rate, there is no incentive to accumulate physical capital. Oil is a natural resource; diesel fuel is a capital good produced by other capital goods, namely, drilling rigs, ships, pipelines, and refineries.

      The notion of organizing an economy with no interest paid is nonsensical on its face. In Muslim banking, for example, they get around the prohibition on usury by having the bank take an equity stake in investments that they finance–an excellent idea. But the interest rate is still their, either explicit or implicit.

      If you want to start a big argument in finance, bring up the question of whether the borrowing rate (cost of capital to the borrower) or the lending rate (cost of financial capital to the lender) should be used in determining “the” discount rate.

      Discount rates are not obvious. Nor are they printed anywhere, in contrast to the Prime Rate, the interest rate on ten-year Treasuries, etc. Determining the correct discount rate to use is of great importance–but our methods of doing so are highly imperfect (and that is being charitable).

  3. majorian says:

    No. It is easy to calculate.
    Annual effective discount rate = effective interest rate -(effective interest rate)^2

    http://en.wikipedia.org/wiki/Discount_rate

  4. Jon Cooksey says:

    I don’t think I agree with Nate’s premise. Discounting is used for dollar values, based on the assumption that inflation will eat away at what the dollar will buy. But (as Charlie Hall and others would point out) the dollar is based on nothing, and should be based on energy, and nothing eats away at the value of energy. In fact, I would argue the opposite: that the value of a barrel of oil or any form of energy will be much much MORE in the future, when they’re scarce, and I don’t mean dollar value – I mean that we devalue energy because we have lots of it, whereas those in the future (who may be us) are going to desperately wish we hadn’t frittered it away flying to Hawaii for vacations, when they can no longer transport their food or heat their house.

    So if anything, I think a sort of negative discounting applies here, which is why we’ll be desperately digging up fossil fuels in the future even if their EROI is stupidly low by today’s standards.

    The same discounting problem applies to human lives, by the way – a human life in the future is valued less than a human life today, implicitly, when evaluating the cost of things like ways to reduce CO2 output. But I’m guessing that the father 2110 will value his daughter just as much as I value mine.

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