The Ergosphere
Friday, February 17, 2006
 

Payback time

One of the major issues of energy policy is EROEI, Energy Return On Energy Invested.  If something consumes more energy than it produces (without some other advantage like portability or compatibility), it isn't worth using.  The greater the EROEI, the better the investment.

Some investments use energy to produce on-going savings.  These have to be measured by a different standard; the investment is up front but the return is over a span of time, so both the rate and duration of the return are important.  The payback may be measured in months to decades.  This complicates matters.  (Fiscal rather than energetic payback is a further complication; prices of some forms of energy are rising faster than the discount rate, which makes future returns more valuable than today's investment rather than less.  I will not try to analyze the price of energy and will restrict this to physics rather than economics.)

The housing stock of the USA varies in efficiency with some of it being fairly good and some being notoriously inefficient (early houses with balloon framing and no insulation, or the cheap stock built in the 1960's being examples).  If these buildings are to be updated, the energy invested in the process must be returned during the remaining lifespan and the faster the better.  But how do you measure either the return or the investment?

When in doubt, guesstimate.  It usually gets to the ballpark, and guesstimates can be refined when you get more data.

The standard for residential construction used to be the exterior wall with 2x4 studs (actually 3-1/2 inches thick) on 16-inch centers with fiberglass insulation and skins of plywood outside and sheetrock inside; it was rated at a nominal R-111, with its actual insulating value being quite a bit lower due to thermal bridging via the studs.  The typical wall actually gets about R-9 per various authorities.  The question becomes, if we have such a wall and want to reduce our net energy consumption, what is the best thing we can do to it?

Insulate the living daylights out of it, of course.  I did some calculations of the heat loss of an unimproved 2x4 stud wall versus the improvements which could be added by re-skinning the house with various thicknesses of solid foam insulation.  (I also just, as in Thursday night, made a pass through Home Depot to check current retail prices and the R-values claimed for the materials.)  If the foam monomer is produced from natural gas and the efficiency of production (weight of foam per weight of gas) is 50%, this table sums up what I got for extruded polystyrene (not beadboard) foam insulation:

Base insulation R-value: 9








Insulation value, R/inch 5








Insulation weight, lb/ft3 1.5








Mfgr efficiency, % 50








Heating value of nat. gas, BTU/lbm 23875































Foam thickness, inches 0 1 2 3 4 5 6 7 8

Foam weight, lbm/ft2 0 0.13 0.25 0.38 0.5 0.63 0.75 0.88 1

Wall R-value 9 14 19 24 29 34 39 44 49
Heating degree-days
Heat loss per square foot of wall, BTU/year
2000
5333 3429 2526 2000 1655 1412 1231 1091 980
3000
8000 5143 3789 3000 2483 2118 1846 1636 1469
4000
10667 6857 5053 4000 3310 2824 2462 2182 1959











Heating degree-days

Energy payback time, years
2000

3.13 4.25 5.37 6.49 7.61 8.73 9.85 10.97
3000

2.09 2.84 3.58 4.33 5.07 5.82 6.57 7.31
4000

1.57 2.13 2.69 3.25 3.81 4.36 4.92 5.48

Types of foam insulation

Polyisocyanurate board is a better insulator than extruded EPS (about R-6.5/inch after aging compared to R-5) and weighs about 2 lbs/ft3 to XEPS's 1.5.  This makes it roughly equal in insulating value to an XEPS board 4/3 as thick; 6 inches of polyisocyanurate is almost exactly equivalent in insulating value to 8 inches of XEPS.  They are also amazingly close in retail price; the optimum cost XEPS board was $17.64 for 4 cubic feet (4 foot by 8 foot by 1.5 inches, R-7.5) while the best-buy polyisocyanurate was $12.34 for 2.67 cubic feet (4 foot by 8 foot by 1 inch, R-6.5).  The polyisocyanurate is very slightly cheaper for the same insulating value, at least in quantity 1.  Which one you'd choose for a given installation would depend more on the immediate price situation and other details (like property taxes from increased "square footage") rather than the specific R-values.

Spray-on urethane does not appear to be even remotely competitive for similar applications.  The kits I found cost around $700 for 50 cubic feet of foam, roughly $14 per cubic foot.  The insulating value is not good enough to justify this cost, but it can be used where rigid board cannot.  Since it is incommensurable with the other two types I will not consider it further.

I did some research on the synthesis of styrene (the monomer for polystyrene) and found that it's derived more from coke-oven products than petroleum per se.  It appears that the raw material for polystyrene may not be affected much by shortages of natural gas or oil.  I had difficulty even finding the molecular structure of isocyanurate monomer (see here), though the nitrogen-carbon ring at the center looked unusual to me; I did not find any hints regarding the typical raw materials for its manufacture.

The payoff

As you can see, the calculated energy payback from the invested fuel is very good; even 8 inches of foam takes a mere 11 heating seasons to pay back its energy of manufacture in an area with 2000 heating degree-days, and just 5 and a half where it's cold enough to make 4000 degree-days.  Unfortunately, the fiscal payback is nowhere near as attractive.  Slapping R-40 of XEPS onto a wall costs roughly $2.94/ft2; under the most severe climactic conditions it would only save about 8700 BTU/year, or 0.087 therms.  If the price of natural gas rises to $1.50/therm it would take over 22 years to pay for itself, exclusive of the cost of structural skins and re-siding.  Even at today's low interest rates, this is not a very attractive investment.  Half that thickness (4 inches, R-20) would save about 11¢/ft2/year at a cost of $1.47/ft2; this would pay off in a bit over 13 years.  At current interest rates, this is moderately attractive.  Greater levels of insulation may pay off faster if combined with a smaller, cheaper heating plant or other economies made possible by the reduced heating load, and tax deductibility of mortgage interest versus operating expenses also adds a bias towards insulation.  This is not a simple calculation.

Conclusion

On a straight EROEI basis, retrofits of foam insulation appear to be a very good investment.  Even the thickest (near-superinsulation) applications will pay off the chemical energy invested in them many times over the life of the structure, and in just a few years in the coldest climates.  The fiscal payback is not nearly so attractive even for the raw materials sans installation costs (at least at retail), unless other factors are considered.

Footnotes:

1. R-value is a measure of resistance to heat transmission, in feet-squared hours degrees-F per BTU.  Divide the temperature difference by the R-value, and you get the heat transmission in BTU per square foot per hour.  The R-value is 1 over the U-value, and vice versa. (back)

 
Comments:
E-P
Interesting that you write this as it is -22 F this morning with 14 mph wind(a -40 F wind chill outside and about a -35 pa inside). . Some thoughts on your analysis concerning some of those other factors.
• As you shift away from a higher heating deg day, energy demand will shift to a higher cooling deg day demand.
• As you tighten a home you decrease the air infiltration losses which can be considerable (estimates range up to 30% to 40% losses) depending on buildings leakage rate(ACH-air changes per hour) and the temperature delta T and pressure delta from interior to exterior.
• The intrinsic heat load by solar gain and the occupants becomes a bigger percentage of a heat factor in a tighter building, this offsets some of the additional supplementary heat in winter, though it does add to the cooling load in summer unless solar shading is used.
• As your heat loss, or gain, is reduced that will change your balance point temperature( the difference in temp between the interior and exterior at which additional heat or cooling input is needed to maintain comfort because of the intrinsic heat load) which will affect the number of heating and cooling deg days which will in turn affect your annual energy usage.
• Also the comfort level will increase (an individual perception, most people can detect a 2 deg temperature difference) mainly due to the slowing of radiant heat loss or gain that we feel (surface temperatures that surround us).

Labor and building design with emphasis on moisture control (keeping the vapor retarder to the warm side of the dew point zone in the insulation) would add to the cost of a retro fit and the payback time but personally I build to try and last 100 years for a life cycle. This house I am in now was 90 when I started the retro fit 12 years ago (due to property lines and legal setbacks the progress has been slow to say the least) I hope someone in the future will give it another 100 years of life after I am gone. I view the fiscal payback time as dependent on the assumptions of the cost of your energy source in the future and the return on the money saved if invested elsewhere. Inflation is factor I have a hard time with so I figure simply that the cost of investing in my building insures that my cost of living will be less in the future. Economics is not my strong point though. But according to my wood pile I use about 4 cords per winter now compared to more than 8 before I started (4 cords of oak at 24-26 mbtu/cord @ 60% efficiency equals 62.4 mbtu which is 624 therms at $1.50/therm is $936.00 in NG equivalent for 1500 sq ft in a 10,000 heating degree day base 65F, latitude) and I only have half the work complete. Most Super Insulated houses will reduce heating and cooling energy use from 60 to 80%, I am still looking for a good link that I can post to support that. As you conclude looking at a single component individually instead of as a system may cause one to marginalize its value too soon and trying to model and quantify a dynamic structure is not simple.

A good book from the past that started me on my quest is
Super Insulated Home Book
By JD Ned Nisson & Gautam Dutt 1985

You can request a free CD or download a simple heat loss calculator from Slant Fin. Fun to play some what ifs with. http://www.slantfin.com/he2/

Geoff
 
I see you're quite comfortable with numbers and unit analysis.  This is something that even evades some students of physics (I could tell stories about someone I tried to tutor once...).  Well done, and don't be afraid to pass that along too.
 
E-P

The RMI approach to building construction/retrofit is to make a building as much like a cave as possible. To do that, you superinsulate (R30 walls, R60 roofs), wrap, and caulk (to eliminate convection losses). To ensure adequate air changes, you install an air to air heat exchanger.

The resultant cave-like environment has a natural ambient temperature somewhere around 55 degrees (ie below frost depth) and responds to outside temperature changes very slowly.

The obvious goal is to make the building so tight and insulated that it doesn't need heating and cooling systems at all. Heating can be accomplished with simple kerosene space heaters. Now, the RMI HQ is in the Rocky Mts and they aren't dealing with humidity issues, so I don't know how this approach would work in a humid environment.
 
Others may differ, but I would not go into a tight-envelope building with an operating kerosene heater in it.  I like my air to have oxygen, and I'm allergic to carbon monoxide.  (If you used a condensing furnace exhausting to the outdoors and sourced the combustion air from the building to get extra ventilation, I'd go for it.)

I'm going to have to find a calculator for heat demand, or some formulae so I can write my own in Javascript.  I think it would be useful to have it as a resource here on The Ergosphere.
 
Great analysis. I wish more people understood this. I wonder how your financial model would look today. Natural gas prices have dropped. Heating oil prices have risen. We are doing something unique with out new home... check out www.GouinGreen.com. Regards, Ed.
 
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